Question

answer it as fast you

Answer 1

√6 +x = x

squaring

6 + x = x^2

x^2 - x-6 = 0

x^2 +2x-3x -6 = 0

x( x+2) -3( x+2)= 0

x= 3,-2

Answer 2

SOLUTION


Value of =>


$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6......... \infty } } } }$

if we look deeply in eq we see that we can put the eq as



$x = \sqrt{6 + x}$


because value is reapeat ..


so proceed now

taking square root both side


${x}^{2} = 6 + x$


Now this eq is look like a quadratic equation


so,

${x}^{2} - x - 6$


ROOTS OF EQ ARE


$= {x}^{2} - 3x + 2x - 6$


$= x(x - 3) + 2(x - 3)$




$=( x - 3) \: and \: (x + 2)$



now values of x are


x=-3

x=-2

but ans is 3


REASON

1) PUT X=-2 IN EQ LET SEE WHAT HAPPENED



$- 2 = \sqrt{6 - 2}$


$- 2 = \sqrt{4}$


-2 not equal to 2

but hay look this both left hand and right hand sides are not equal