Question

If a-b=7 and a^3-b^3=133 then find ab and a square+b square

Answer 1

Hey Mate ✌

Here's your answer,

Given : (a - b) = 7 ..............(1)

a³ - b³ = 133 .......................(2)

==> LHS = a³ - b³

==> a³ - b³ = ( a - b)( a² + ab + b²)

==> 133 = (a - b)( a² + ab + b²) ......from (2)

==> 133 = (7)(a² + ab + b²) ............from (1)

==> 133 / 7 = a² + ab + b²

==> 19 = a² + ab + b²

==> a² + ab + b² = 19

is the required answer ^_^

⭐ Hope you got your answer ⭐

Answer 2

Answer:

a+b=7

a^3+b^3=133

a^2+b^2=?

(a+b)^2=a^2+b^2+2ab

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

7^3=133+3ab(a+b)

343-133=3ab(7)

210=3ab(7)

3ab=30

ab=10

therefore,

(a+b)^2=a^2+b^2+2ab

49=a^2+b^2+20

a^2+b^2=29

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