If-a-gt-b-gt-0-and-4a-2-b-2-4ab-Find-a-b-a-b-

Question Number 206477 by hardmath last updated on 15/Apr/24

If a > b > 0 and {4 a}^{2} + b^{2} = 4 ab

Find : \frac{a - b}{a + b} = ?

Answered by MATHEMATICSAM last updated on 16/Apr/24

4 a^{2} + b^{2} = 4 a b

\Rightarrow 4 a^{2} - 4 a b + b^{2} = 0

\Rightarrow {(2 a - b)}^{2} = 0

\Rightarrow 2 a - b = 0

\Rightarrow 2 a = b

\Rightarrow \frac{a}{b} = \frac{1}{2}

\Rightarrow \frac{a + b}{a - b} = \frac{1 + 2}{1 - 2} = - 3 [Comp . and Div .]

\Rightarrow \frac{a - b}{a + b} = - \frac{1}{3} (Ans)

Answered by A5T last updated on 15/Apr/24

4 a^{2} - 4 a b + b^{2} = 0

\Rightarrow a = \frac{4 b \underline{+} \sqrt{16 b^{2} - 16 b^{2}}}{8} = \frac{b}{2}

\Rightarrow \frac{a - b}{a + b} = \frac{- \frac{b}{2}}{\frac{3 b}{2}} = \frac{- 1}{3}

Answered by Rasheed.Sindhi last updated on 15/Apr/24

{4 a}^{2} - 4 ab + b^{2} = 0

{(2 a - b)}^{2} = 0

b = 2 a

\frac{a - b}{a + b} = \frac{a - 2 a}{a + 2 a} = \frac{- a}{3 a} = - \frac{1}{3}