Question

a^2+b^2=69,a^4+b^4=3409 then find a^3+b^3=

Answer 1

Answer

a² + b² = 69 .....(1)

a⁴ + b⁴ = 3409 ......(2)

a³ + b³ = ?

squaring both sides of equation ....(1)

we get

(a²+b²) = a⁴ + b⁴ + 2a²b²

put the values from above equations

(69²) = 3409 + 2(ab)²

4761 - 3409 = 2(ab)²

1352/2 = (ab)²

676 = (ab)²

ab = 26

we know

(a+b)² = a² + b² + 2ab

put the value that we have found along with given value.

(a+b)² = 69 + 2(26)

(a+b)² = 121

(a+b) = 11

now

we know

(a+b)³ = a³ + b³ + 3ab(a+b)

put all the values that we have found.

(11)³ = a³ + b³ + 3(26)(11)

1331 - 572 = a³ + b³

a³ + b³ = 759

hope this will help you