If √(x) + 1over√(x) = 7, then the value of x\ +\ 1over x is equal t8o:

If √(x) + 1over√(x) = 7, then the value of x\ +\ 1over x…

If $\sqrt x$ + $1\over{\sqrt x}$ = 7, then the value of $x\ +\ {1\over x}$ is equal t8o:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. 47.

We know that,

(a + b)² = a² + b² + 2ab

$\sqrt x$ + $1\over{\sqrt x}$ = 7

Squaring both sides

⇒ ( $\sqrt x$ + $1\over{\sqrt x}$ )² = 7²

⇒ ( $\sqrt x$ )² + ( $1\over{\sqrt x}$ )² + 2 × $1\over{\sqrt x}$ × $\sqrt x$ = 49

⇒ x + $1\over{x}$ + 2 = 49

⇒ x + $1\over{x}$ = 47