Question

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

Answer 1

(x + y)² = x²  + y² + 2xy

Take away 2xy from both sides:

(x + y)² - 2xy  = x²  + y²

Switch sides:

x² + y² = (x + y)² - 2xy

Sub x + y = 9 and xy = 16:

x² + y² = (9)² - 2(16)

Evaluate:

x² + y² = 81 - 32

x² + y² = 49

Answer: 49

Answer 2

Step-by-step explanation:

Answer:

(x + y) = 9

xy = 16

(x² + y²) = ?

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

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

⠀

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