Question

If a – 1 a = 7, evaluate a⁴ + 1 a⁴ .​

Answer 1

Answer:

2599

Step-by-step explanation:

Given, a - 1/a = 7

  Square on both sides:

⇒ (a - 1/a)² = 7²

⇒ a² .+ 1/a² - 2(a * 1/a) = 49

⇒ a² + 1/a² - 2(1) = 49

⇒ a² + 1/a² = 51

     Square on both sides(again):

⇒ (a² + 1/a²)² = 51²

⇒ a⁴ + 1/a⁴ + 2(a² * 1/a²) = 2601

⇒ a⁴ + 1/a⁴ + 2(1) = 2601

⇒ a⁴ + 1/a⁴ = 2599

Answer 2

Answer:

Given :-

• $a - \frac{1}{a} = 7$

□To find :-

• Evaluating
• ${a}^{4} + 1 {a}^{4}$

□Solution :-

• Here by squaring the equation on both sides we get that,
• $(a - 1 {a)}^{2} = {7}^{2} = {a}^{2} + \frac{1}{a} {}^{2} - 2(a \times \frac{1}{a} ) = 49$
• ${a}^{2} + \frac{1}{a } {}^{2} - 2 = 49 = {a}^{2} + \frac{1}{a} {}^{2} = 51$
• Squaring on both sides we get that,

• ${a}^{4} + \frac{1}{a} {}^{4} + 2( {a}^{2} \times \frac{1}{a} {}^{2} ) = 2601 = {a}^{4} + \frac{1}{a} {}^{4} + 2 = 2601$
• ${a}^{4} + \frac{1}{a} {}^{4} = 2599$

For more information :-

• https://brainly.in/question/44294996.
• search on web.

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