Question

i need help solving this problem 64d^3=100d?

Answer 1

`d=0" or "d=+-5/4`

Explanation:

Rearrange the equation and equate to zero.

`rArr64d^3-100d=0`

Take out a `color(blue)"common factor"` of 4d

`rArr4d(16d^2-25)=0rarr(1)`

`16d^2-25"` is a `color(blue)"difference of squares"` and factorises, in general, as follows.

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^2-b^2=(a-b)(a+b))color(white)(2/2)|)))`

`"here "a=4d" and "b=5`

`rArr16d^2-25=(4d-5)(4d+5)`

Returning to (1) and completing.

`rArr4d(4d-5)(4d+5)=0`

Solving each of the 3 factors.

`4d=0rArrd=0`

`4d-5=0rArrd=5/4`

`4d+5=0rArrd=-5/4`

`rArrd=0" or " d=+-5/4" are the solutions"`