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Algebra and Applications Test 2

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Question : 9 of 40

Marks: +1, -0

If

u^2 = gv + hw

v^2 = fu + w^2 = fu + gv

; then what is the expression

\frac{1}{u+f} + \frac{g}{v+g} + \frac{h}{w+h}

equal to?

$\frac{1}{u} + \frac{1}{v} + \frac{1}{w}$
1
-1
0
None of these

Solution: 👈: Video Solution

u^2 = gv + hw

\Rightarrow u^2 + fu = fu + gv + hw

\Rightarrow u(u+f) = fu + gv + hv

\Rightarrow \frac{1}{u+f} = \frac{u}{fu + gv + hw}

\Rightarrow \frac{f}{u+f} = \frac{fu}{fu + gv + hw}

......(i)

Also,

v^2 = hw + fu

\Rightarrow v^2 + gv = fu + hw + gv

\Rightarrow v(v+g) = fu + hw + gv

\Rightarrow \frac{g}{v+g} = \frac{gv}{fu + hw + gv}

......(ii)

and

w^2 = fu + gv

\Rightarrow w^2 + hw = fu + hw + gv

\Rightarrow w(w+h) = fu + hw + gv

\Rightarrow \frac{h}{w+h} = \frac{hw}{fu + hw + gv}

......(iii)

Adding (i), (ii) and (iii) we get,

\frac{fu}{fu+gv+hw} + \frac{gv}{fu + hw + gv} + \frac{hw}{fu + hw + gv}

= \frac{fu+gv+hw}{fu+gv+hw} = 1

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