Question

If (x - 1)3 = 8 and (y - 2)2 = 16 ,find (x + y )^2

Answer 1

Step-by-step explanation:

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

●(x - 1)3 = 8

●(y - 2)2 = 16⠀⠀⠀

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

$(x+y)^2$

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

(x-1)3=8

3x-3=8

3x=8+3

3x=11

$\boxed{\pink{x=\frac{11}{3}}}$

then..

(y-2)2=16

2y-4=16

2y=16+4

2y=20

$\boxed{\pink{y=\frac{\cancel{20}}{\cancel{2}}=10}}$

Then find the value of $(x+y)^2$

=$(\frac{11}{3}+10)^2$

=$(\frac{11+30}{3})^2$

=$(\frac{41}{3})^2$

=$\frac{1681}{9}$

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

$\sf{\underline{\mathcal\color{gold}{(x+y)^2=\frac{1681}{9}}}}$

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