Question

if (x+y) = 9 and xy = 16, find the value of x square + Y square

Answer 1

(x+y) =9
(x+y) ^2 =81
x^2 +y^2 +2xy=81
x^2 +y^2 +2(16)=81 (x*y=16)
x^2 +y^2 +32=81
x^2 +y^2 =49

Answer 2

$\sf \underline{correct \: question \: } :$

• if (x -y) = 9 and xy = 16, find the value of x square + Y square

(x - y) = 9

xy = 16

(x² + y²) = ?

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$\dashrightarrow\sf (x-y)=9\\\\{\scriptsize\qquad\bf{\dag}\:\:\texttt{Squaring Both Sides -}}\\\\\dashrightarrow\sf (x-y)^2=(9)^2\\\\\\\dashrightarrow\sf (x)^2+(y)^2-2xy=(9 \times 9)\\\\\\\dashrightarrow\sf x^2+y^2-(2 \times 16)=81\\\\\\\dashrightarrow\sf x^2+y^2-32=81\\\\\\\dashrightarrow\sf x^2+y^2=81+32\\\\\\\dashrightarrow\underline{\boxed{\sf x^2+y^2=113}}$

⠀

$\therefore\:\underline{\textsf{Required Answer will be a) \textbf{113}}}.$