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

1/{u+f}+g/{v+g}+h/{w+h}

equal to?

$1/u+1/v+1/w$
1
-1
0
None of these

Solution:

u^2 = gv + hw

⇒u^2+fu = fu+gv + hw

⇒u(u+f)=fu+gv+hv

⇒1/{u+f}=u/{fu+gv+hw}

⇒f/{u+f}={fu}/{fu+gv+hw}

......(i)
Also,

v^ 2 = hw + fu

⇒ v^ 2 + gv = fu + hw + gv

⇒ v (v + g) = fu + hw + gv

⇒ g/ (v + g) ={gv}/ {fu + hw + gv}

......(ii)
and

w^2 = fu + gv

⇒ w^2 + hw = fu + hw + gv

⇒ w (w + h) = fu + hw + gv

⇒ h/ (w + h) ={hw}/{ fu + hw + gv}

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

{fu}/{fu+gv+hw}+{gv}/ {fu + hw + gv}+{hw}/{ fu + hw + gv}

={fu+gv+hw}/{fu+gv+hw}=1

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