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Gaurav Seth 6 years, 3 months ago
The largest number by which x , y divisible and gives the remainder a , and b is the HCF of ( x - a ) and ( y - b)
__________________________
According to the given problem ,
The largest number which divides 70 and 125 leaving remainders 5 and 8 respectively are
HCF of ( 70 - 5 ) = 65 and
( 125 - 8 ) = 117
65 = 5 × 13
117 = 3 × 3 × 13
HCF ( 65 , 117 ) = 13
Required number is 13.
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Yogita Ingle 6 years, 3 months ago
Let p(x) = 3x²-2kx+2m
Given, 2 & 3 are zeroes of p(x).
Then , p (2) = 0 & p(3)= 0
Now, p(2)= 3×2²-2k(2)+2m=0
3× 4-4kx+2m=0
12-4k+2m=0………..(1)
p(3) = 3×3²-2k(3)+2m=0
3× 9-6kx+2m=0
27-6k+2m=0………..(2)
On Subtracting Equation 1 from equation 2.
27-6k+2m=0
12-4k+2m=0
(-) (+) (-)
------------------
15-2k =0
15=2k
k= 15/2
On putting k= 15/2 in eq 1
12-4k+2m=0
12-4(15/2)+2m=0
12-30+2m=0
-18+2m=0
2m=18
m=18/2
m=9
Hence, k=15/2, m= 9
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Yogita Ingle 6 years, 3 months ago
X + y = 5 ( equation 1 )
2x - 3y = 4 ( equation 2 )
Now,
multiplying (eq.1) by 2 and subtracting (eq.2) from ( eq.1 )
(2x + 2y = 10) - (2x - 3y = 4 )
=> 2x + 2y - 2x + 3y = 6
=> 5y = 6
=> y = 6/5
Putting the value of y in ( eq.1 )
=> x+ y = 5
=> x + 6/5 = 5
=> x = 5 - 6/5
=> x = 19/5

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Sachin Mahto 6 years, 3 months ago
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