If x2-y2-25- y- then - x-y-5 -

We have, #10; #10;If x^2+y^2=25y #10; #10;Then, #10; #10; [ x y5]=? #10; #10;From given, #10; #10; x^2+y^2=25y #10; #10; ...

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Byju's Answer

Standard XII

Mathematics

Composite Function

If x2+y2=25...

Question

If $x^{2} + y^{2} = 25 \times y, t h e n [\frac{x - y}{5}]$ =

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Solution

We have,

If $x^{2} + y^{2} = 25 y$

Then,

$[\frac{x - y}{5}] = ?$

From given,

$x^{2} + y^{2} = 25 y$

$\Rightarrow \frac{x^{2} + y^{2}}{25} = y$

$\Rightarrow \frac{x^{2} + y^{2} + 2 x y - 2 x y}{25} = y$

$\Rightarrow \frac{{(x - y)}^{2} + 2 x y}{25} = y$

$\Rightarrow \frac{{(x - y)}^{2}}{25} + \frac{2 x y}{25} = y$

$\Rightarrow {(\frac{x - y}{25})}^{2} = y - \frac{2 x y}{25}$

$\Rightarrow {(\frac{x - y}{25})}^{2} = \frac{25 y - 2 x y}{25}$

$\Rightarrow \frac{x - y}{5} = \sqrt{\frac{25 y - 2 x y}{25}}$

$\Rightarrow \frac{x - y}{5} = \frac{\sqrt{25 y - 2 x y}}{5}$
Hence, this is the answer.

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If x2+y2=25×y,then[x−y5]=

We have, If x2+y2=25y Then, [x−y5]=? From given, x2+y2=25y ⇒x2+y225=y ⇒x2+y2+2xy−2xy25=y ⇒(x−y)2+2xy25=y ⇒(x−y)225+2xy25=y ⇒(x−y25)2=y−2xy25 ⇒(x−y25)2=25y−2xy25 ⇒x−y5=√25y−2xy25 ⇒x−y5=√25y−2xy5 Hence, this is the answer.

If $x^{2} + y^{2} = 25 \times y, t h e n [\frac{x - y}{5}]$ =