Question

mathematics problem

quadratic equation solve

first answer brainliest
25 points

#answerasap

Answer 1

Answer:

x = -2, x = 7

Step-by-step explanation:

Given: [1/(x-1)(x-2)] + [1/(x-2)(x-3)] + [1/(x-3)(x-4)] = 1/6

LCM = 6(x-1)(x-2)(x-3)(x-4)

⇒ 6(x-3)(x-4) + 6(x-1)(x-4) + 6(x-1)(x-2) = (x-1)(x-2)(x-3)(x-4)

⇒ 6x²-42x+72+6x²-30x+24+6x²-18x+12=x⁴-10x³+35x²-50x+24

⇒ 18x²- 90x + 108 = x⁴ - 10x³ + 35x² - 50x + 24

⇒ 18x² = x⁴ - 10x³ + 35x² - 50x + 24 - 18x² - 108 = 0

⇒ x⁴ - 10x³ + 17x² + 40x - 84 = 0

⇒ x⁴ - 12x³ + 2x³ + 41x² - 24x² - 42x + 82x - 84 = 0

⇒ x⁴ - 12x³ + 41x² - 42x + 2x³ - 24x² + 82x - 84 = 0

⇒ x(x³ - 12x² + 41x - 42) + 2(x³ - 12x² + 41x - 41) = 0

⇒ (x + 2)(x³ - 12x² + 41x - 42) = 0

⇒ (x + 2)(x³ - 10x² - 2x² + 21x + 20x - 42) = 0

⇒ (x + 2)(x(x² - 10x + 21) - 2(x² - 10x + 21)) = 0

⇒ (x + 2)(x - 2)(x² - 10x + 21) = 0

⇒ (x + 2)(x - 2)(x² - 3x - 7x + 21) = 0

⇒ (x + 2)(x - 2)(x(x - 3) - 7(x - 3)) = 0

⇒ (x + 2)(x - 2)(x - 3)(x - 7) = 0

⇒ x = -2,2,3,7

Verification:

Substitute x values in denominator.

x = 2:

1/(x-2)(x-3) = 1/(2-2)(2-3) = 0

x = 3:

1/(x-2)(x-3) = 1/(3-2)(3-3) = 0.

Hence, x cannot be 2,3.

Therefore, the values of x are -2,7.

Hope it helps!