Question

If 3x+ 5y +4z =0 , prove that 27x³ +125y³ +64z³=180xyz​

Answer 1

We know

If a+b+c=0

`\boxed{\sf a^3+b^3+c^3=3abc}`

`\\ \sf\longmapsto 3x^3+5y^3+4z^3=3(3x)(5y)(4z)`

• Simplify

`\\ \sf\longmapsto 27x^3+125y^3+64z^3=180xyz`

Hence proved

Answer 2

Use the following identity:

• a³ + b³ + c³ = 3abc if a + b + c = 0

Substitute:

• a = 3x, b = 5y, c = 4z

and get:

• (3x)³ + (5y)³ + (4z)³ = 3(3x)(5y)(4z)
• 27x³ + 125y³ + 64z³ = 180xyz