Question
If $a + b = 7$ and $ab = 10;$ 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 $a+b=7 ; a b=10$
Substitute the values of $(a+b)$ and $(ab)$ in equation $(1),$ we have
$(a-b)^2 =(7)^2-4(10)$
$ =49-40=9$
$\Rightarrow a-b = \pm \sqrt{9}$
$\Rightarrow a-b = \pm 3$
$(a+b)^2=a^2+2 a b+b^2$
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 $a+b=7 ; a b=10$
Substitute the values of $(a+b)$ and $(ab)$ in equation $(1),$ we have
$(a-b)^2 =(7)^2-4(10)$
$ =49-40=9$
$\Rightarrow a-b = \pm \sqrt{9}$
$\Rightarrow a-b = \pm 3$
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