Question

If a^3-b^3=513 and ab=54, then prove that a-b=3

Answer 1

Answer:

Let a - b be 3,

So LHS and RHS must be equal,

To check :

➡ ( a - b )³ = 3³, is true

➡ (a-b)³ = 27, is true

➡ a^3 - b^3 - 3ab(a-b) = 27, is true

➡ a^3 - b^3 - 3(54)(3) = 27, is true

➡ 513 - 486 = 27, is true

➡ 27 = 27, which is true.

Hence proved.

Properties used: ( x - y )^3 = x^3 - y^3 - 3xy( x - y )

Answer 2

Answer:

a^3+b^3=513,ab=54,a-b=?