Using the properties of proportion, solve for x, given \frac{x^4+1}{2 x^2}=\frac{17}{8}

ICSE Class X Math 2013 Solved Paper - Question 45

Question : 45 of 46

Marks: +1, -0

Using the properties of proportion, solve for

x

, given

\;{x^4+1}/{2 x^2}=\;{17}/{8}

Solution:

Given:

\;{x^4+1}/{2 x^2}=\;{17}/{8}

By using componendo and dividendo, we get

\;{x^4+1+2 x^2}/{x^4+1-2 x^2}\;=\;{17+8}/{17-8}

(\;{x^2+1}/{x^2-1}) ^2\;=\;{25}/{9}

(\;{x^2+1}/{x^2-1}) ^2\;= (\;{5}/{3}) ^2

Taking square root on both sides, we get

\;\;{x^2+1}/{x^2-1}\;=\;{5}/{3}

⇒ 5 x^2-5\;=3 x^2+3

⇒ 5 x^2-3 x^2\;=3+5

⇒ 2 x^2\;=8

⇒ x^2\;=4

⇒ x\;= ± 2

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