Question

Question #d8fb4

Answer 1

The Soln. Set`={4, -7/2, (1+-sqrt65)/4}.`

Explanation:

`(2x-7)(x^2-9)(2x+5)-91=0`.

`:.{(2x-7)(x+3)}{(x-3)(2x+5)}-91=0`

`:. (2x^2-7x++6x-21)(2x^2-6x+5x-15)-91=0`

`:. (2x^2-x-21)(2x^2-x-15)-91=0`

`:. (y-21)(y-15)-91=0", where, "y=2x^2-x`

`:. y^2-36y+315-91=0`

`;. y^2-36y+224=0`

`:. ul(y^2-28y)-ul(8y+224=0`

`:. y(y-28)-8(y-28)=0`

`:. (y-28)(y-8)=0`

Returning `y`, (2x^2-x-28)(2x^2-x-8)#.

`:. {ul(2x^2-8x)+ul(7x-28)}(2x^2-x-8)=0`.

`:. {2x(x-4)+7(x-4)}(2x^2-x-8)=0`

`:. (x-4)(2x+7) (2x^2-x-8)=0`

`:. x=4, or, x=-7/2, or, 2x^2-x-8=0`
,
To find the zeroes of `(2x^2-x-8)=0`, we use the Quadratic Formula & get the Zeroes : `(1+-sqrt((-1)^2-4(2)(-8)))/(2*2)=(1+-sqrt65)/4`.

Thus, the Soln. Set`={4, -7/2, (1+-sqrt65)/4}.`

Enjoy Maths.!