Question

Find the nature of the roots of equation (x2 + 1)2 – x2 = 0.​

Answer 1

Answer:

$\Large\boxed{\mathsf{X=-1}}$

Step-by-step explanation:

GIVEN:

Find the nature of the roots of equation of (x2+1)2-x2=0 from left to right numbers.

Isolate by the x from one side of the equation.

SOLUTIONS:

$\displaystyle \mathsf{\left(x* \:2+1\right)*\:2-x*\:2=0}}}}$

First, expand by using with distributive property.

Distributive Property

A(B+C)=AB+AC

$\displaystyle \mathsf{(X*2+1)*2-x*2}}}$

$\displaystyle \mathsf{2\left(2x+1\right)-2x}$

Multiply numbers from left to right.

2(X*2+1)

A=2

B=X*2

C=1

2x*2+2*1

2*2x+2*1

Solve.

$\displaystyle \mathsf{2*2x+2*1=4x+2}$

Rewrite the problem.

4x+2-x*2

Solve.

$\displaystyle \mathsf{4x+2-x*2=2x+2}$

$\displaystyle \mathsf{2x+2=0}$

Subtract by 2 from both sides.

$\displaystyle \mathsf{2x+2-2=0-2}$

Solve.

$\displaystyle \mathsf{2x=-2}$

Then, divide by 2 from both sides.

$\displaystyle \mathsf{\frac{2x}{2}=\frac{-2}{2}  }$

Solve.

$\displaystyle \mathsf{-2\div2=\boxed{-1}}$

$\Large\boxed{\mathsf{X=-1}}}}}}$

So, the correct answer is x=-1.

Answer 2

Answer:

Rewrite the propiem.

4x+2-x*2

Solve.

4x+ 2 x 2 = 2x + 2

2x+2=0

Subtract by 2 from both sides.

2x+2 2 0 - 2

Solve.

2x = -2

Then, divide by 2 from both sides.

2x -2

2 2

Solve.

-2÷2= -1