Question

$x^{2} \sqrt{x} ¡$

Answer 1

Answer:

Math

5 points

Solution!!

→ x - 2√x - 8 = 0

Move the expression to the right-hand side and change its sign

→ -2√x = 8 - x

Square both sides of the equation

→ (-2√x)² = (8 - x)²

→ (-2)²(√x)² = (8)² + (x)² - 2(8)(x)

→ 4x = 64 + x² - 16x

Move the expression to the left-hand side and

change its sign

→ - x² + 4x + 16x - 64 = 0

Factor out -x and 16 from the expression

→ - x(x - 4) + 16(x - 4) = 0

Factor out -x + 16 from the expression

→ (- x + 16)(x - 4) = 0

Now atleast one of the factors is zero.

→ - x + 16 = 0

→ x - 4 = 0

→ x = 16

→ x = 4

Now, let's check if the value is the solution of the equation.

→ 16 - 2√16 - 8 = 0

→ 4 - 2√4 - 8 = 0

→ 16 - 2(4) - 8 = 0

→ 4 - 2(2) - 8 = 0

→ 16 - 8 - 8 = 0

→ 4 - 4 - 8 = 0

→ 16 - 16 = 0

→ 4 - 12 = 0

→ 0 = 0

→ -8 ≠ 0

Hence, the value of x is 16.

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