What is the answer to sqrt(1+x*\sqrt{x^2+24)}=x+1 ?

The answer to sqrt(1+x*\sqrt{x^2+24)}=x+1 is x=0,x=5

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sqrt(1+x*\sqrt{x^2+24)}=x+1

1 + x \cdot x^{2} + 24 = x + 1

x = 0, x = 5

Solution steps

1 + x x^{2} + 24 = x + 1

Square both sides:

1 + x x^{2} + 24 = x^{2} + 2 x + 1

1 + x x^{2} + 24 = x^{2} + 2 x + 1

Subtract

x^{2} + 2 x + 1

from both sides

1 + x x^{2} + 24 - (x^{2} + 2 x + 1) = x^{2} + 2 x + 1 - (x^{2} + 2 x + 1)

Simplify

- x^{2} + x^{2} + 24 x - 2 x = 0

Factor

- x^{2} + x^{2} + 24 x - 2 x : - x (x - x^{2} + 24 + 2)

- x (x - x^{2} + 24 + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - x^{2} + 24 + 2 = 0

Solve

x - x^{2} + 24 + 2 = 0 : x = 5

x = 0, x = 5

Verify Solutions:

x = 0

True

, x = 5

True

The solutions are

x = 0, x = 5

f, v = \frac{( f \cdot 1 )}{m}

x^{2} - 4 2 x + 6 = 0

3 x - 2 - 11 = 0

x = 5 + x + 1

x + 2 = 7

What is the answer to sqrt(1+x*\sqrt{x^2+24)}=x+1 ?
The answer to sqrt(1+x*\sqrt{x^2+24)}=x+1 is x=0,x=5
Solve for x: sqrt(1+x*\sqrt{x^2+24)}=x+1
The solution is x=0,x=5