Question

if a + b is equal to 1 and a minus b is equal to 7 find a square + b square and a b

Answer 1

-a-b)^2=(a+b)^2-4ab(7)^2=( a+b)^2-4(9)49+36=(a+b)^2(a+b)^2=85

Answer 2

Answer -


$\binom{(a + b) = 1}{(a - b) = 7} \\ \\ solve \: for \: a \\ \\ \binom{(a + b) = 1}{a = 7 + b} \\ \\ substitute \: the \: value \: of \: a \: into \: a + b = 1 \\ \\ 7 + b + b = 1 \\ \\ 7 + 2b = 1 \\ \\ 2b = 1 - 7 \\ \\ 2b = - 6 \\ \\ b = \frac{ - 6}{2} \\ \\ b = - 3$

$substitute \: the \: value \: of \: b \: into \: a = 7 + b \\ \\ a = 7 - 3 \\ \\ a = 4$


Now, (a,b) = (4,-3)

Therefore,

${a}^{2} + {b}^{2} = \\ \\ = 4 {}^{2} + ( - 3 {)}^{2} \\ \\ = > 4 {}^{2} = 4 \times 4 = 16 \\ \\ - 3 {}^{2} = - 3 \times - 3 = 9 \\ \\ 16 + 9 = 25 \\ \\ a b = \\ 4 \times - 3 = - 12$


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