Question

If a+b=8 and a2+b2=34 find a3+b3

Answer 1

solution

(a+b)2=a2 +b2 +2ab

(8)2= 34+2ab

64=34+2ab

64-34=2ab

30= 2ab

30÷2=ab

15=ab

(a+b)3= a3+ b3+3ab (a+b)

(8)3= a3+b3+3*15(a+b)

(8)3= a3+b3+ 45(a+b)

(8)3=a3+b3+45*8

(8)3=a3+b3+360

(8)3-360=a3+b3

512-360=a3+b3

152=a3+b3

Answer 2

Answer:a^3+b^3= 152

Step-by-step explanation:

a + b= 8

Now, a^2 + b^2 = (a + b)^2 - 2ab

34 = 64- 2ab

-2ab =34-64

-2ab=-30

2ab=30 (both negetive cancelled)

ab=30/2

ab=15

a^3 + b^3 = (a + b)3 - 3ab (a + b)

a^3 + b^3 = 512 - 3 x ab x 8

= 512 - 360 = 152(substitute the value of ab)

a^3+b^3= 152