Question

Solve this..
$\tt{} \sqrt{7+ \sqrt{7 + \sqrt{7+ \sqrt{7 + \sqrt{7+ \sqrt{7} ...} } } } } = x$
find the value of x ?​

Answer 1

✓7+9= ✓16

✓16=4

therefore value of x might be 9

Answer 2

3 is the answer

Step by step explanation :

$\sf Let, \tt{} \sqrt{7+ \sqrt{7 + \sqrt{7+ \sqrt{7 + \sqrt{7+ \sqrt{7} ...} } } } } = x$

$⟹ \sqrt{7 + \sqrt{7 - x} } = x$

Squaring the both sides .

We will , get

$7 + \sqrt{7 - x} = x {}^{2}$

$\sqrt{7 - x = } x {}^{2} - 7$

Again squaring

$x⁴ - 14x² + x + 42 = 0$

Hence, the expression will be 3 is the answer .