Question

If X-Y = 7 and XY= -1 than the value of (X+Y)² is​

Answer 1

THEREFORE YOUR ANSWER IS 45.

I hope you are satisfied by my answer.

Answer 2

Answer :

$\large{ \star\:\:\boxed{\bf{x^{2}\:\:+\:\:y^{2}\:\:=\:\:45}}\:\:\star }$

Explanation :

Given :–

• x - y = 7
• (x) × (y) = xy = (-1)

To Find :–

• The numerical value of (x + y)²

Formula Applied :–

• $\boxed{\star\:\:\bf{(a\:-\:b)^2\:=\:a^2\:-\:2ab\:+\:b^2}\:\:\star}$

• $\boxed{\star\:\:\bf{(a\:+\:b)^2\:=\:a^2\:+\:2ab\:+\:b^2}\:\:\star}$

Solution :–

We have,

• x - y = 7
• xy = (-1)

Putting these values in the Formula :

$\rightarrow\sf{(x\:-\:y)^2\:=\:x^2\:-\:2xy\:+\:y^2}$

$\rightarrow\sf{(7)^2\:=\:x^2\:-\:[2\:\times\:(-1)]\:+\:y^2}$

$\rightarrow\sf{49\:=\:x^2\:-\:(-2)\:+\:y^2}$

$\rightarrow\sf{49\:=\:x^2\:+\:2\:+\:y^2}$

$\rightarrow\sf{x^2\:+\:y^2\:=\:49\:-\:2}$

$\rightarrow\sf{x^2\:+\:y^2\:=\:47}$

Now , we have ,

• x² + y² = 47
• xy = (-1)

Putting these values in the Formula :

$\rightarrow\sf{(x\:+\:y)^2\:=\:x^2\:+\:2xy\:+\:y^2}$

$\rightarrow\sf{(x\:+\:y)^2\:=\:(x^2\:+\:y^2)\:+\:2xy}$

$\rightarrow\sf{(x\:+\:y)^2\:=\:(47)\:+\:[2\:\times\:(-1)]}$

$\rightarrow\sf{(x\:+\:y)^2\:=\:47\:-\:2}$

$\rightarrow\boxed{\bf{(x\:+\:y)^2\:=\:45}}$

∴ The value of x² + y² is 45 .