Question
If $m - n = 0.9$ and $mn = 0.36$, find:$m + n$
✓
Answer
Given $m - n = 0.9$ and $mn = 0.36$
$(m - n)^2 = m^2 - 2mn + n^2$
$\Rightarrow (0.9)^2 = m^2 - 2mn + n^2$
$\Rightarrow 0.81 = m^2 + n^2 - 2(0.36)$
$\Rightarrow 0.81 = m^2 + n^2 - 0.72$
$\Rightarrow m^2 + n^2 = 1.53$
So, $(m + n)^2 = m^2 + 2mn + n^2$
$\Rightarrow (m + n)^2= m^2 + n^2 + 2mn$
$\Rightarrow (m + n)^2 = 1.53 + 2(0.36)$
$\Rightarrow (m + n)^2 = 2.25$
$\Rightarrow m + n = ± 1.5.$
$(m - n)^2 = m^2 - 2mn + n^2$
$\Rightarrow (0.9)^2 = m^2 - 2mn + n^2$
$\Rightarrow 0.81 = m^2 + n^2 - 2(0.36)$
$\Rightarrow 0.81 = m^2 + n^2 - 0.72$
$\Rightarrow m^2 + n^2 = 1.53$
So, $(m + n)^2 = m^2 + 2mn + n^2$
$\Rightarrow (m + n)^2= m^2 + n^2 + 2mn$
$\Rightarrow (m + n)^2 = 1.53 + 2(0.36)$
$\Rightarrow (m + n)^2 = 2.25$
$\Rightarrow m + n = ± 1.5.$
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