Question

If a + b = 6 and ab = 15then a³+b³=? ​

Answer 1

Answer:

a3 + b3 = (a + b)3 – 3ab ( a + b)

= (8)3 – 3(15) (8) = 512 – 360 = 152

Answer 2

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Step-by-step explanation: Here we know that a=6+b so we can say that a = b = 6 and ab = 15, and now we - have to find a²+b² and a³-b³

a-b=6

a³-b³ = (a-b) (a² + ab + b²)

Here we have the values of a-b (which equals 6) and we also know that

ab =15, so lets find a² + b²

a-b=6

(Now lets square both sides)

(a-b)² = 6²

a² -2ab + b² = 36

Now we know that (ab = 15)( So 2ab = 30)

a² - 30+ b² = 36

a² + b² = 36 + 30

a² + b² = 66

Now we know that a² + b² = 66 so we can find the value of a³-b³ now.

a³-b³ = (a-b) (a² + ab + b²)

Now we know that a - b = 6 and a² + b² = 66 and ab = 15 So now we will substitute the values

a³-b³ = (6) (a² + b² + ab)

a³-b³=(6)(66 +15)

a³-b³ = (6) (a² + b² + ab)

a³-b³ = (6)(81)

a³-b³ = 486

Therefore a³- b³ = 486 and a² + b² = 66