Question

(X^-3x-10) (x^-5x-6) =144

Answer 1

(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