UPSC CDS 1 2022 Math Paper

Given:
x+‌

1

x

=‌

5

2

‌‌⋯(i)
Formula Used:
(a+b)2=a2+b2+2ab
Calculation:
We have to find the value of ‌

5x

7x2−3x+7

Taking x common from the denominator, we get
‌

5x

x(7x−3+‌ 7 x )

⇒‌

5

(7x+‌ 7 x −3)

⇒‌

5

(7[x+‌ 1 x ]−3)

From (i)
⇒‌

5

7×‌ 5 2 −3

=‌

10

35−6

⇒‌

10

29

∴ The required value of the expression is ‌

10

29

.