Question

Question #52ae1

Answer 1

`k=+-5/2`

You have `4x^2-8kx+9=0`
and you know that the two solutions, `x_2 and x_1`, are related as:
`x_2-x_1=4`

You solve your equation with `k` in place:
`x_(1,2)=(8k+-sqrt(64k^2-4(4*9)))/8`
Giving:
`x_(1,2)=(8k+-sqrt(64k^2-144))/8`
These are two solutions: one with the + sign and the other with the - sign. Substituting in: `x_2-x_1=4` you get
`(8k+sqrt(64k^2-144))/8-(8k-sqrt(64k^2-144))/8=4`
rearranging and taking as common denominator `8` you'll get:
`2*(sqrt(64k^2-144))=32`
`(sqrt(64k^2-144))=16`
`64k^2-144=256`
`k=sqrt(400/64)=+-5/2`