Question
If $ a - b = 7$ and $ab = 18;$ find $a + b.$
✓
Answer
We know that,
$(a-b)^2=a^2-2 a b+b^2$
and
$ (a+b)^2=a^2+2 a b+b^2$
Rewrite the above equation, we have
$(a+b)^2=a^2+b^2-2 a b+4 a b$
$=(a+b)^2+4 a b\ldots(1)$
Given that $a-b=7 ; a b=18$
Substitute the values of ( $a-b)$ and $(ab)$ in equation $(1),$ we have
$(a+b)^2 =(7)^2+4(18)$
$ =49+72=121$
$\Rightarrow a+b = \pm \sqrt{121}$
$\Rightarrow a+b$
$=\pm 11$
$(a-b)^2=a^2-2 a b+b^2$
and
$ (a+b)^2=a^2+2 a b+b^2$
Rewrite the above equation, we have
$(a+b)^2=a^2+b^2-2 a b+4 a b$
$=(a+b)^2+4 a b\ldots(1)$
Given that $a-b=7 ; a b=18$
Substitute the values of ( $a-b)$ and $(ab)$ in equation $(1),$ we have
$(a+b)^2 =(7)^2+4(18)$
$ =49+72=121$
$\Rightarrow a+b = \pm \sqrt{121}$
$\Rightarrow a+b$
$=\pm 11$
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