Question

x + y = 14 and xy = 16. Find the value of x2 +y2

Answer 1

Answer :-

$\large{\underline{\boxed{\sf {x}^{2} + {y}^{2} = 164}}}$

Explanation :-

Given :

• x + y = 14
• xy = 16

Solution :

We know that,

• (x + y)² = x² + y² + 2xy

By putting the values, we get :-

$\sf\longrightarrow {(14)}^{2} = {x}^{2} + {y}^{2} + 2 \times 16$

$\sf\longrightarrow 196 = {x}^{2} + {y}^{2} + 32$

$\sf\longrightarrow 196 - 32 = {x}^{2} + {y}^{2}$

$\sf\longrightarrow 196 - 32 = {x}^{2} + {y}^{2}$

$\sf\longrightarrow 164 = {x}^{2} + {y}^{2}$

$\boxed{\therefore{\sf {x}^{2} + {y}^{2} = 164}}$

Answer 2

$\huge { \red {\underline{ \frak{Your \: answEr :}}}}$

$\huge{\boxed{ \star \: \bold{ {x}^{2} + {y}^{2} = 164 }}}$

$\huge { \red {\underline{ \frak{Explanation :}}}}$

$\large { \underline{ \mathcal{Given :}}}$

• x + y = 14
• x + y = 14xy = 16

$\large { \underline{ \mathcal{To \: \: Find :}}}$

Q. Find the Value of (x² + y²).

$\large { \underline{ \mathcal{Solution :}}}$

$\green{\boxed{ \tt {We~Know~that~(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy }}$

★ Plugging in the Values ;

$\large{\Rightarrow \tt{ {(14)}^{2} = {x}^{2} + {y}^{2} + (2 \times 16) }}$

$\scriptsize \pink{\blacksquare \tt{ \: \: {x + y = 14 \: \: and \: \: xy = 16}}}$

$\large{\Rightarrow \tt{196 = {x}^{2} + {y}^{2} + 32}}$

$\large{\Rightarrow \tt{ {x}^{2} + {y}^{2} = 196 - 32}}$

$\purple{\huge\boxed {\Rightarrow \tt {x}^{2} + {y}^{2} = 164}}$