Question

Find the value -1 =?" alt="a^6+6a^2b^2+b^2-1 =?" align="absmiddle" class="latex-formula">
If $a^2+b^2=2$

Answer 1

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.

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