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Show that square of any odd integer is of the form 4m+1 for some integer m.

Posted by Mohankrishna Nayak 6 years, 10 months ago

2 answers

Gaurav Seth 6 years, 10 months ago

Let a be any positive integer and b = 4
Then, by Euclid''s algorithm a = 4q + r for some integer q 0 and 0 r < 4
Since, r = 0, 1, 2, 3
Therefore, a = 4q or 4q + 1 or 4q + 2 or 4q + 3

Since, a is an odd integer, o a = 4q + 1 or 4q + 3

Case I: When a = 4q + 1

Squaring both sides, we have,
a² = (4q + 1)²
a² = 16q² + 1 + 8q
= 4(4q² + 2q) + 1
= 4m + 1 where m = 4q² + 2q

Case II: When a = 4q + 3

Squaring both sides, we have,
a² = (4q +3)²
    = 16q² + 9 + 24q
    = 16 q² + 24q + 8 + 1
    = 4(4q² + 6q + 2) +1
    = 4m +1 where m = 4q² +7q + 2

Hence, a is of the form 4m + 1 for some integer m.

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Sneha Singh 6 years, 10 months ago

Refer ncert

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Find the value of a so the point (3, a) lies on the line represent by 2x -3y=5

Posted by Rituraj Jadav Mali 5 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Sejal ??? 6 years, 10 months ago

a=1/3

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If the roots of the quadratic equation (a square +b square )x square - 2(ac+bd)x+(c square +d square)=0 are equal ,prove that a/b=c/d

Posted by Gauri ❤ 6 years, 10 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

4 theroms

Posted by Aryan Chopdar 6 years, 10 months ago

CBSE > Class 10 > Mathematics

0 answers

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2-cosec^2/cosec^2+cot^2=sin-cos/sin+cos

Posted by Appu Enterprises 6 years, 10 months ago

CBSE > Class 10 > Mathematics

0 answers

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If 7cosecA-3cotA=7 prove that 7cotA-3cosecA =3

Posted by Richa Prashar 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Appu Enterprises 6 years, 10 months ago

Search this question on google.

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All formule of ch 13

Posted by Sahil Singh 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Sneha Singh 6 years, 10 months ago

U should check on this app click on ch13 then open cbse revision notes u will get all the formulas of ch13

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Honey ??? 6 years, 10 months ago

Use google

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Given HCF (396,82)=2 find LCM (396,82)=?

Posted by Rehan Khan 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Nishu Dewangan 6 years, 10 months ago

HCF×LCM=product of two number 2×LCM=396×82 2×LCM= 30258 LCM=30258/2 LCM=15129

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Which term of the A.P: 21,18,15,....is -81? Also,is any term 0?

Posted by Sejal Malhotra 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Honey ??? 6 years, 10 months ago

8th term is 0

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Rahul Kuntal Jaat Sahab 6 years, 10 months ago

An=a+(n-1)d -81=21+(n-1)-3 -81-21=(n-1)-3 -102=(n-1)-3 -102÷-3=n-1 34=n-1 34+1=n 35=n

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Find the distance of the point P(-6,8) from the origin?

Posted by Sukhdev Bhardwaj 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Rahul Singh 6 years, 10 months ago

As origin is O(0,0) Then distance of OP is OP^2 = (X2-X1)^2+(Y2-y1)^2 = (-6-o) ^2 + (8-O)^2 = (-6)^2 + (8)^2 = 36 + 64 =loo OP = √Ioo op= lo = Ans

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If 3sin + 5cos=5. Prove that 5sin - 3cos=±3

Posted by Naman Goyal 6 years, 10 months ago

CBSE > Class 10 > Mathematics

0 answers

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Through the midpoint M of the side CD of a parallelogram ABCD,the line BM is drawn intersecting AC at L and AD produced at E. Prove that EL=2BL

Posted by Sandhya Sridhar 6 years, 10 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Pythgarous theorem

Posted by Arbiya Banu 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Shivam Tripathi 6 years, 10 months ago

Study from any reference

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Cosec square b+c/2 -tan square a/2=1 if ABC are interior angel of triangle abc

Posted by Sanjeev Kumar 6 years, 10 months ago

CBSE > Class 10 > Mathematics

0 answers

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Q.Prove that BPT THEROM.

Posted by Shivam Verma 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Ziya Olympiad Academy Gurudhan 6 years, 10 months ago

BPT we can prove by Similarity between Triangles also...My dear students This prove may be important in Board exam once think and prove bpt by Similar triangles concept.

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Gaurav Seth 6 years, 10 months ago

BPT(Thales Theorem) -

Given - In triangle ABC, DE is parallel to BC. DE bisects AB at D and AC at E.

To Prove - AD/BD= AE/CE

Construction - Join BE and CD and draw EF is perpendicular to AB and DG is perpendicular to AC.

Proof -

As, EF is perpendicular to AB, EF is the height of tr's ADE and DBE.

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Please give me chapter wise marks chat of math

Posted by Suhan Mohanty 6 years, 10 months ago

CBSE > Class 10 > Mathematics

3 answers

Rose? Choudhary ? 6 years, 10 months ago

Number system = 6 marks.......... Algebra = 20 marks........... Coordinate geometry = 06 marks............. Geometry = 15 marks....... Trigonometry = 12 marks........ Mensuration = 10 marks ........ Statistics and probability = 11 marks......

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Ash? The King? 6 years, 10 months ago

Ch. 1=6marks Ch.2=3mrk 3=5mrk 4=5mrk 5=7mrk 6=8mrk 7=4mrk 8=8mrk 9=4mrk 10=3mrk 11=4mrk 12=3mrk 13=7mrk 14=7mrk 15=4mrk

3Thank You

Lol No 6 years, 10 months ago

Every time marking scheme differs .... Even the no. Of questions differ....

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7x+7 -4=0

Posted by Ashish Zehen 6 years, 10 months ago

CBSE > Class 10 > Mathematics