Respuesta :

SalmonWorldTopper

Answer:

The value of a⁶ + 6a²b² + b⁶ -1 = 7.

Step-by-step explanation:

Correct question: Find the value of a⁶ + 6a²b² + b⁶ -1 = ? If a²+b² = 2

Explanation:

Given that: a² + b² = 2 – – – Equation(1)

On cubing both sides then

⇛(a² + b²)³ = 2³

Compare the LHS with (x + y)³, we get

x = a² and y = b²

Using identity (x + y)³ = x³ + y³ + 3xy(x+y), we have

⇛(a² + b²)³ = 2³

⇛(a²)³ + (b²)³ + 3a²b² (a² + b²) = 2*2*2

⇛a⁶ + b⁶ + 3a²b² (a² + b²) = 8

Since, from equation (1) a²+b² = 2 (Given)

⇛a⁶ + b⁶ + 3a²b² (2) = 8

⇛a⁶ + b⁶ + 6a²b² = 8

On subtracting 1 from both sides

⇛a⁶ + b⁶ + 6a²b² - 1 = 8-1

Therefore, a⁶ + 6a²b² + b⁶ -1 = 7

Answer: Hence, the value of a⁶ + 6a²b² + b⁶ -1 = 7.

Please let me know if you have any other questions.

The value of the expression a⁶ + 6a²b² + b⁶ - 1  is; 7

How to expand Algebraic expressions?

We are given;

a² + b² = 2 – – – Eq (1)

Taking the cube of both sides gives;

(a² + b²)³ = 2³

Compare the Left hand side with (x + y)³ gives;

x = a²

y = b²

With the aid of algebraic identity of (x + y)³ = x³ + y³ + 3xy(x+y), we have

(a² + b²)³ = 2³

⇒ (a²)³ + (b²)³ + 3a²b² (a² + b²) = 2³

⇒ a⁶ + b⁶ + 3a²b² (a² + b²) = 8

Substituting 2 for a²+b² gives;

a⁶ + b⁶ + 3a²b²(2) = 8

a⁶ + b⁶ + 6a²b² = 8

Subtract 1 from both sides to get;

a⁶ + b⁶ + 6a²b² - 1 = 8 - 1

Thus;

a⁶ + 6a²b² + b⁶ - 1 = 7

Read more about algebraic expansion at; https://brainly.com/question/4344214

Otras preguntas