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Abhishek Kumar 7 years, 5 months ago

38 is divisible by 2 and 45 is divisible by 5 that's why it is not prime no.
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Sia ? 6 years, 6 months ago

LCM(p,q) = a3b3
and HCF(p,q) = a2b
LCM(p,q) {tex}\times{/tex} HCF(p,q) = a3b3 {tex}\times{/tex} a2b

{tex}\begin{array}{l}\mathrm{LCM}(\mathrm p,\mathrm q)\;\times\mathrm{HCF}(\mathrm p,\mathrm q)\;=\mathrm a^5\mathrm b^4\;-----(1)\\\mathrm{and}\;\mathrm{pq}=\mathrm a^2\mathrm b^3\;\times\mathrm a^3\mathrm b=\mathrm a^5\mathrm b^4\;------(2)\\\mathrm{from}\;\mathrm{eq}^\mathrm n\;(1)\;\mathrm{and}\;(2)\\\mathrm{LCM}(\mathrm p,\mathrm q)\;\times\mathrm{HCF}(\mathrm p,\mathrm q)\;\;=\mathrm{pq}\\\\\end{array}{/tex}

 

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Sia ? 6 years, 6 months ago

Let {tex} \alpha , \beta , \gamma{/tex} be the zeroes of polynomial f(x) = x3 - 5x2 - 2x + 24 such that {tex} \alpha\beta{/tex} = 12.
{tex} \alpha + \beta + \gamma = - \left( - \frac { 5 } { 1 } \right) = 5{/tex} ................ (i)
{tex} \alpha \beta + \beta \gamma + \gamma \alpha = \frac { - 2 } { 1 } = - 2{/tex}
and, {tex} \alpha \beta \gamma = - \frac { 24 } { 1 } = - 24{/tex}
Putting, {tex} \alpha \beta = 12{/tex} in {tex} \alpha \beta \gamma = - 24{/tex}, we get
{tex} 12 \gamma = - 24{/tex}
{tex} \Rightarrow \gamma = - \frac { 24 } { 12 } = - 2{/tex}
Putting {tex} \gamma= -2{/tex} in eq.(i), we get
{tex} \alpha + \beta - 2 = 5{/tex}
{tex} \Rightarrow \quad \alpha + \beta = 7{/tex}
Now, {tex} ( \alpha - \beta ) ^ { 2 } = ( \alpha + \beta ) ^ { 2 } - 4 \alpha \beta{/tex}
{tex} \Rightarrow \quad ( \alpha - \beta ) ^ { 2 } = 7 ^ { 2 } - 4 \times 12{/tex}
{tex} \Rightarrow \quad ( \alpha - \beta ) ^ { 2 } = 1{/tex}
{tex} \Rightarrow \quad \alpha - \beta = \pm 1{/tex}
Thus, we have
{tex} \alpha + \beta= 7{/tex}  and {tex} \alpha - \beta = 1 {/tex} or, {tex} \alpha + \beta= 7{/tex} and {tex} \alpha - \beta= -1{/tex}
CASE I: When {tex} \alpha + \beta= 7{/tex} and {tex} \alpha - \beta= 1{/tex}
Solving {tex} \alpha + \beta= 7{/tex} and {tex} \alpha - \beta= 1{/tex} , we get
{tex} \alpha = 4{/tex} and {tex}\beta= 3{/tex} 
CASE II: When {tex} \alpha + \beta= 7{/tex} and {tex} \alpha - \beta= -1{/tex}
Solving {tex} \alpha + \beta= 7{/tex} and {tex} \alpha - \beta= -1{/tex} , we get
{tex} \alpha = 3{/tex} and {tex}\beta= 4{/tex} .
Hence, the zeros of the given polynomial are 3, 4 and - 2 or 4,3 , -2.

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Sia ? 6 years, 6 months ago

Yes, you can check the syllabus here : https://mycbseguide.com/cbse-syllabus.html

2-7
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Arohi . 7 years, 5 months ago

Are you just checking does it work or you are a kid.

Priya Kumari 7 years, 5 months ago

-5
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Akshata Kondi 7 years, 5 months ago

Cbse 8question paper
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Mr. Shashank 7 years, 5 months ago

X=5 & Y =6
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Sia ? 6 years, 6 months ago

{tex}30 = 2 \times 3 \times 5{/tex}
{tex}{72=8×9=2}^3\times3^2{/tex}
{tex}{432=16×27=2}^4\times3^3{/tex}
Therefore, HCF  = 2 {tex}\times{/tex} 3 = 6
LCM  {tex}= 2^4 \times 3^3 \times 5 = 2160{/tex}

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Anwaya Kumar Nayak 7 years, 5 months ago

Which chapter
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Sia ? 6 years, 6 months ago

Given: In the figure, ABC and AMP are two right triangles, right angled at B and M respectively,

To prove:

  1. {tex}\triangle {/tex}ABC {tex} \sim {/tex} {tex}\triangle {/tex}AMP
  2. {tex}\frac{{CA}}{{PA}} = \frac{{BC}}{{MP}}{/tex}

Proof:

  1. In {tex}\triangle {/tex}ABC {tex} \sim {/tex} {tex}\triangle {/tex}AMP
    {tex}\angle{/tex}ABC = {tex}\angle{/tex}AMP (1) ........ [Each equal to 90o]
    {tex}\angle{/tex}BAC={tex}\angle{/tex}MAP (2).........[Common angle]
    In view of (1) and (2)
    {tex}\triangle {/tex}ABC {tex} \sim {/tex} {tex}\triangle {/tex}AMP ..........AA similarity criterion
  2. {tex}\triangle {/tex}ABC {tex} \sim {/tex} {tex}\triangle {/tex}AMP.........Proved above in(i)
    {tex}\therefore {/tex} {tex}\frac{{CA}}{{PA}} = \frac{{BC}}{{MP}}{/tex}.........Corresponding sides of two similar triangles are proportional.
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Abhishek Reddy 7 years, 5 months ago

Google
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Abhishek Reddy 7 years, 5 months ago

Send the correct information
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A. Tiwari 7 years, 5 months ago

x+y=7...... (1) 5x+2y=7....... (2) ------------------------- Equation (1)×5 Equation (2)×1 {By elimination method} We'll get 5x+5y=35......... (3) 5x+2y=7...........(4) --------------------------------- [On subtracting equation 3 and 4] We'll get, 3y=28 y=28/3 On putting the value of y in equation (1) x+y=7 x+(28/3)=7 x=7-28/3 x=(-7/3)

Ayush Kashyap 7 years, 5 months ago

Please answer me

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