If \sqrt{5+x} + \sqrt{5–x} }/{ \sqrt{5+x} – \sqrt{5–x} }=7, then what is the value of x?

SSC CPO SI and ASI Model Paper 2

Question : 110 of 200

Marks: +1, -0

If ${√{5+x} + √{5–x} }/{ √{5+x} – √{5–x} }=7$ , then what is the value of x?

Solution:

√{{ 5+x} + {5–x}}/√{{5+x }– {5–x}}=7

⇒√{ 5 + x }+ √{5 - x} =

7 √{5 + x} - 7√ {5 - x}

⇒8 √{5- x} = 6 √{5 + x}⇒ =

4 √{5 - x }=3 √{5 + x}

By squaring both sides, we have:

16 (5 – x) = 9 (5 + x)

⇒ 80 – 16x = 45 + 9x
⇒25x = 35

⇒ x = 7/5

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