Question

if a-b=4 and a+B=6; find a^2+b^2​

Answer 1

Answer:

Given,

$a + b = 6 \\ a - b = 4 \\ {a}^{2} + {b}^{2} = \: to \: \: find \\ we \: know \: that \: \\ \: \: \: \: \: \: \: \: 2( {a}^{2} + {b}^{2} ) = {(a + b})^{2} + {(a - b)}^{2} \\ \implies \: 2( {a}^{2} + {b}^{2} ) = {6}^{2} + {4}^{2} \\ \implies \: 2( {a}^{2} + {b}^{2} ) = 36 + 16 \\ \implies \: 2( {a}^{2} + {b}^{2} ) = 52 \\ \implies \: ( {a}^{2} + {b}^{2} ) = \frac{52}{2} \\ \implies \: ( {a}^{2} + {b}^{2} ) = 26$