If -12-12-12-x- then the value of x is -

The correct option is A 4 √(12+√(12+√(12+....))) = x .........................(1) √(12+x)=x (12+x)=x^2 x^2 x 12=0 (x 4)(x+3)=0 ...

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Standard XII

Mathematics

Definition of Relations

If √12+√12+...

Question

If $\sqrt{(12 + \sqrt{12 + \sqrt{12 + . . . .}})} = x$ , then the value of x is ____________.

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Solution

The correct option is A $4$
$\sqrt{12 + \sqrt{12 + \sqrt{12 + . . . .}}} = x$ .........................(1)
$\sqrt{12 + x} = x$
$(12 + x) = x^{2}$
$x^{2} - x - 12 = 0$
$(x - 4) (x + 3) = 0$
$x = 4$ or $x = - 3$
since x is a positive number (eq 1)
$x = 4$

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If √(12+√12+√12+....)=x, then the value of x is ____________.

The correct option is A 4√12+√12+√12+....=x.........................(1)√12+x=x(12+x)=x2x2−x−12=0(x−4)(x+3)=0x=4 or x=−3since x is a positive number (eq 1)x=4

If $\sqrt{(12 + \sqrt{12 + \sqrt{12 + . . . .}})} = x$ , then the value of x is ____________.

The correct option is A $4$
$\sqrt{12 + \sqrt{12 + \sqrt{12 + . . . .}}} = x$ .........................(1)
$\sqrt{12 + x} = x$
$(12 + x) = x^{2}$
$x^{2} - x - 12 = 0$
$(x - 4) (x + 3) = 0$
$x = 4$ or $x = - 3$
since x is a positive number (eq 1)
$x = 4$