Question

if x-y = 9 and xy = 16 then
find x²+y²​

Answer 1

Answer:

113

Explanation:

(x-y)^2=x²+y²-2xy;

xy=16;

2xy=2×16,

now:

(9)^2=x²+y²-2×16,

81=x²+y²-32,

81+32=x²+y²

113=x²+y²

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Answer 2

Explanation:

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

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

• (x - y) = 9

• xy = 16

• (x² + y²) = ?

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

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

⠀

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