If $$a+2b = 10$$, $$2ab = 9$$, then $$|a-2b| = $$

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Uniteasy Admin · Accepted Answer

Given condition 
$$a+2b = 10$$n
Square both sides of the equation
$$(a+2b)^2 = 100$$
Expand the LHS
$$a^2+4b^2+2\cdot 2ab = 100 $$
then,
$$a^2+4b^2 = 100-2\cdot 2ab = 100-2\cdot 9 = 82 $$
that is
$$a^2+4b^2 =82$$n
On the other hand, construct an equation using the conjugate of $$a+2b$$
$$(a+2b)^2+(a-2b)^2 = 2(a^2+4b^2)$$n
Substituting (1) and (2) results in
$$(a-2b)^2 = 2\cdot 82-100=64$$
Therefore
$$|a-2b| = 8$$
D is the correct option

Multiple Choice Question (MCQ)

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