Question

√x+4 +2 = x. solve for x

Answer 1

Answer:

Step-by-step explanation:

Given equation - ✓x+4+2=x

Or, ✓x+6=x

Or, x=✓x+6

Or, x-6=√x {transporting 6 to RHS}

Or, (x-6)²=(✓x)² {squaring both sides}

Or, (x)²-2(x)(6)+(6)²=x { since (a-b)²=a²-2ab+b²}

Or, x²-12x+36=x

Or, x²-12x-x+36=0 {transporting X to LHS}

Or, x²-13x+36=0

Or, x²-(9+4)x+36=0 {by splitting middle term}

Or, x²-9x-4x+36=0

Or, x(x-9)-4(x-9)=0

Or, (x-4)(x-9)=0 -------eq(1)

Therefore if eq(1) is equal to 0 then

Either x-4=0. Or x-9=0

Therefore either x=4 or x=9

But x=4 is not possible.

Therefore X=9

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