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ICSE Class X Math 2013 Solved Paper

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Question : 45
Total: 46
Using the properties of proportion, solve for x, given
‌
x4+1
2x2
=‌
17
8
Solution:  
Given: ‌
x4+1
2x2
=‌
17
8

By using componendo and dividendo, we get
‌
x4+1+2x2
x4+1−2x2
‌=‌
17+8
17−8

(‌
x2+1
x2−1
)2‌=‌
25
9

(‌
x2+1
x2−1
)2‌=(‌
5
3
)2
Taking square root on both sides, we get
‌‌
x2+1
x2−1
‌=‌
5
3

⇒5x2−5‌=3x2+3
⇒5x2−3x2‌=3+5
⇒2x2‌=8
⇒x2‌=4
⇒x‌=±2
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