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ICSE Class X Math 2013 Paper

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Question : 45 of 46
Marks: +1, -0
Using the properties of proportion, solve for xx, given
  x4+12x2=  178\;\frac{x^4+1}{2x^2}=\;\frac{17}{8}
Solution:  
Given:   x4+12x2=  178\;\frac{x^4+1}{2x^2}=\;\frac{17}{8}
By using componendo and dividendo, we get
  x4+1+2x2x4+1−2x2  =  17+817−8\;\frac{x^4+1+2x^2}{x^4+1-2x^2}\;=\;\frac{17+8}{17-8}
(x2+1x2−1)2  =  259\left(\frac{x^2+1}{x^2-1}\right)^2\;=\;\frac{25}{9}
(x2+1x2−1)2  =(53)2\left(\frac{x^2+1}{x^2-1}\right)^2\;= \left(\frac{5}{3}\right)^2
Taking square root on both sides, we get
    x2+1x2−1  =  53\;\;\frac{x^2+1}{x^2-1}\;=\;\frac{5}{3}
⇒5x2−5  =3x2+3\Rightarrow 5x^2-5\;=3x^2+3
⇒5x2−3x2  =3+5\Rightarrow 5x^2-3x^2\;=3+5
⇒2x2  =8\Rightarrow 2x^2\;=8
⇒x2  =4\Rightarrow x^2\;=4
⇒x  =±2\Rightarrow x\;= \pm 2
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