Question

Solve the equation (x+2)^2+(x−1)^2 =(x+5)^2 using the Pythagorean theorem.

a) x = -4
b) x = -1
c) x = 2
d) x = 5

Answer 1

Neither 'x = -4', 'x = -1', 'x = 2', nor 'x = 5' are correct solutions for the given equation. After expanding and simplifying the equation, the potential solutions are 'x = 10' and 'x = -2', which are not present in the provided options.

Step-by-step explanation:

To solve the equation (x+2)^2+(x−1)^2 =(x+5)^2 using the Pythagorean theorem, we first expand each squared term.

Expanding the left side:

• (x+2)^2 = x^2 + 4x + 4
• (x-1)^2 = x^2 - 2x + 1

Expanding the right side:

• (x+5)^2 = x^2 + 10x + 25

Now, combining the expanded left terms and setting them equal to the expanded right term:

• x^2 + 4x + 4 + x^2 - 2x + 1 = x^2 + 10x + 25

Combine like terms:

• 2x^2 + 2x + 5 = x^2 + 10x + 25

Subtracting x^2 + 10x + 25 from both sides to set the equation to zero:

• x^2 - 8x - 20 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring:

• (x - 10)(x + 2) = 0

Setting each factor equal to zero gives us two potential solutions:

• x - 10 = 0 → x = 10 (not listed among the choices)
• x + 2 = 0 → x = -2 (again, not listed)

Given the choices provided, none of the solutions are listed. Therefore, the correct choice would likely be that the problem has been stated incorrectly or there was a typo in the options provided.