Question

√30+√30
$\sqrt{30 + \sqrt{30 + \sqrt{30 + \sqrt{30........ \infty } } } }$

Answer 1

HEY USER !!

HERE IS YOURS SOLUTION;

◆ Let, √30 .........∞ be x.

So, we reconstruct the given equation;

x = √30 √30 .....∞

◆ Now, we square both the sides, So, we get;

$x {}^{2} = 30 \: + \: x \\ \\ x {}^{2} - x - 30 = 0 \\ \\ now \: we \: the \: concept \: of \: middle \: term \: split \\ \\ = > x {}^{2} - 6x + 5x - 30 = 0 \\ \\ = > x(x - 6) + 5(x - 6) = 0\\ \\ = > (x + 5)(x - 6) = 0\\ \\ = > x = - 5 \: or \: 6$

★ So, the value of X is -5 & 6 ★

HOPE IT HELPS

Answer 2

$\bf\huge\red{\fbox{\fbox{answer}}}$

let a= $\sqrt({30} +\sqrt{30} .....)$

a = √30+a

a2= 30+a

a(a-1)=30

a=6 or -5

now, root can never be negative

a=6