Question

the value of x²+y² if x-y=3 and xy=10​

Answer 1

Answer:

$\purple {{{\sf 29 }}}$

Step-by-step explanation:

To Find:

${x}^{2} + {y}^{2}$

if :

$x - y = 3 \: \: \: \: \: \: xy = 10 \\ \tiny\texttt{ • Now } \\ x - y = 3 \\ x = 3 + y \: ➝ \: 1 \: \: \: and \: \: \: xy = 10 \: ➝ \: 2 \\ \\ \tiny\texttt{ • substuite \: x \: value from \: eqn \: 1 \: in \: eqn \: 2 } \\ = (3 + y)y - 10 \\ \\ 3y + {y}^{2} = 10 \\ \\ {y}^{2} + 3y - 10 \\ \\ {y}^{2} + 5y - 2y - 10 \\ \\ y(y + 5) - 2(y + 5) \\ \\ (y - 2) \: \: (y + 5) \\ \\ y = 2 \: \: \: y = - 5 \\ \\ \tiny\texttt{ • y = 2 \: substuite \: in \: eqn \: 1 } \\ x = 3 + 2 \\ x = 5 \\ \\ = {x}^{2} + {y}^{2} \\ = {5}^{2} +{2}^{2}\\ = 25 + 4 \\ = 29$