Question

If a+b=11 and a³+b³=737 find a²+b² Plz write if you know the answer

Answer 1

✯Given:-

a+b = 11

a³+b³=737

✯To Find:-

a²+b²

✯Solution:-

First we will find ab

We know that,

(a+b)³ = a³+b³+3ab(a+b)

Using this identity,

(11)³ = 737 + 3ab(11)

1331 = 737 + 33ab

33ab= 1331 - 737

33ab= 594

ab = 18

Now , we will find a²+b²

We know that,

a²+b² = (a+b)² - 2ab

Using this identity,

a²+b²=(a+b)² - 2ab

a²+b²=(11)² - 2(18)

a²+b²=121-36

a²+b²=85

Therefore, a²+b²=85

Hope it helps.

✯More Info:-

We can use one more identity as well to find a²+b² here.

We know that, a³+b³ = (a+b)(a²+b²- ab)

Using this identity,

737 = (11)(a²+b² - 18)

737 = 11(a²+b²) - 198

11(a²+b²) = 737+198

11(a²+b²)=935

a²+b² = 935÷11

a²+b²=85