Question

ax + by = a - b
bx - ay = a + b
Simultaneous Equations
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Answer 1

suppose x= sqrt(3+ sqrt (3+ sqrt (3 + sqrt (3+….infinity))))

so, the equation will be : x= sqrt (3+x)

$\sf \: x^2 =3+x$

It will form a quadratic equation,as below

$\sf \: (x)^2 -x -3=0</p><p>$

It can be solved by simple method of factors,

$\sf \: (x)^2 -3x+1x-3=0</p><p>$

$\sf \: x(x-3)+1(x-3)=0$

$\sf \: (x+1)(x-3)=0$

so, the two factors are 3,-1.

Thus, x can have value of 3 or -1. Both value satisfies the above equation.