If x-y - 7 and xy - 10- then the value of x2-y22xy-9 will be

Given, x+y=7 On squaring both side we get, (x+y)^2=7^2 On applying identity we get, ⇒ x^2+2xy+y^2=49 ⇒ x^2+2× 10+y^2=49 nbsp; nbsp; nbsp; [Given xy=1 ...

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Byju's Answer

Standard VIII

Mathematics

Application of Identity: (x+y)^2

If x+y = 7 an...

Question

If $x + y = 7$ and $x y = 10$ , then the value of $\frac{(x^{2} + y^{2})}{2 x y + 9}$ will be

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Solution

Given,
$x + y = 7$

On squaring both side we get,
$(x + y)^{2} = 7^{2}$

On applying identity we get,
$\Rightarrow x^{2} + 2 x y + y^{2} = 49$

$\Rightarrow x^{2} + 2 \times 10 + y^{2} = 49$
[Given $x y = 10$ ]

$\Rightarrow x^{2} + y^{2} = 49 - 20$

$\Rightarrow x^{2} + y^{2} = 29$

On dividing both side by $2 x y + 9$ we get,
$\Rightarrow \frac{x^{2} + y^{2}}{2 x y + 9} = \frac{29}{2 \times 10 + 9}$

$\Rightarrow \frac{x^{2} + y^{2}}{2 x y + 9} = \frac{29}{29} = 1$

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If x+y=7 and xy=10, then the value of (x2+y2)2xy+9 will be

Given, x+y=7 On squaring both side we get, (x+y)2=72 On applying identity we get, ⇒x2+2xy+y2=49 ⇒x2+2×10+y2=49 [Given xy=10] ⇒x2+y2=49−20 ⇒x2+y2=29 On dividing both side by 2xy+9 we get, ⇒x2+y22xy+9=292×10+9 ⇒x2+y22xy+9=2929=1

If $x + y = 7$ and $x y = 10$ , then the value of $\frac{(x^{2} + y^{2})}{2 x y + 9}$ will be