Question

Find the value of root 30+ root30+root30......

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Answer 1

Answer:

hi the answer will be

X = 6

Hope it helps

Answer 2

The roots are $x = -5 , 6$

Step-by-step explanation:

Let the unknown value be x

Then we can write

$x = \sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+...}}}}$

Then we can also write

​$x = \sqrt{30+x}$

​Taking square of both the sides, we will obtain

$x^2=30+x$

Shifting the terms on one side, we obtain

$x^2-x-30 = 0$

It is a quadratic equation in the variable x.

Thus, using middle term splitting method, factorizing the quadratic equation, we obtain

$x^2-6x+5x-30 = 0$

Taking common terms outside brackets

$x(x-6)+5(x-6) = 0$

$(x+5)(x-6) = 0$

Thus, the roots are $x = -5 , 6$