(X^-3x-10) (x^-5x-6) =144
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(x² - 3x - 10)(x² - 5x - 6) = 144 => x= 7 , 2 , - 3
Step-by-step explanation:
(x² - 3x - 10)(x² - 5x - 6) = 144
=> (x - 5)(x + 2)(x - 6)(x + 1) = 144
144 = 1 * 2 * 2 * 2 * 2 * 3 * 3
As we can see two terms having odd numbers & Two terms having even number
Hence two odd Factors must be 9 & 1 ( as 3 , 3 does not give any solution)
x + 2 = 9 & x - 6 = 1 => x = 7
Lets try to solve by solving equation
(x² - 3x - 10)(x² - 5x - 6) = 144
=> x⁴ - 8x³ - x² + 68x + 60 = 144
=> x⁴ - 8x³ - x² + 68x - 84 = 0
=> (x - 7)(x³ - x² - 8x + 12) = 0
=> (x - 7) (x - 2)(x² + x - 6) =0
=> (x - 7)(x - 2)( x + 3)(x - 2) =0
=> x= 7 , 2 , - 3
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