Question

If a+b=1 and a² +b² = 2, then find the value of a³ + b³.​

Answer 1

Answer:

Step-by-step explanation:

Given that,

a + b = 1 and a² + b² = 2

∴ a³ + b³ = ( a + b ) ( a² + b² - ab )

= ( 1 ) ( 2 - ab )

= 2 - ab is the answer.

Answer 2

Concept:

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

(a+b)² =a² + b²+2ab

(a+b)³ =a³ + b³+3a²b+3ab²

a³ + b³ = ( a + b ) ( a² + b² - ab )

a³ - b³ = ( a - b ) ( a² + b² +ab )

Given:

If a+b=1 and a² +b² = 2,

Find:

then find the value of a³ + b³.​

Solution:

a + b = 1 and a² + b² = 2

a³ + b³ = ( a + b ) ( a² + b² - ab )

= ( 1 ) ( 2 - ab )-----------------------i

(a+b)² =a² + b²+2ab

1= 2+2 ab

ab=-1/2

So, using this value in eq i

a³ + b³=2+1/2

            =5/2

Therefore,  a³ + b³=5/2

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