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The number of soulution to the equation |x|(6x2 + 1) = 5x2 is

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Best answer

Calculation:

Condition 1

When x > 0

⇒ x × (6x2 + 1) = 5x2

⇒ 6x3 - 5x2 + x = 0

⇒ x(6x2 - 5x + 1) = 0

⇒ x(3x - 1)(2x - 1) = 0

So the value of x is 0, 1/2, and 1/3  (x ≠ 0)

Condition 2

When x ≤  0

⇒ -x × (6x2 + 1) = 5x2

⇒ 6x3 + 5x2 + x = 0

⇒ x(6x2 + 5x + 1) = 0

⇒ x(2x + 1)(3x + 1) = 0

So the value of x is 0, -1/2, and -1/3

∴ There are 5 different values of x which are 0, -1/2, 1/2, -1/3, and 1/3.

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