Math, asked by sparhead007, 7 months ago

solve : X²-2ax + a² -1 = 0 ​

Answers

Answered by anindyaadhikari13
3

Required Answer:-

Given:

  • x² - 2ax + a² - 1 = 0

To Find:

  • The values of x.

Solution:

Given,

➡ x² - 2ax + (a² - 1) = 0

➡ x² - (2a)x + (a + 1)(a - 1) = 0

➡ x² - (a + a)x + (a + 1)(a - 1) = 0

➡ x² - (a + 1 + a - 1)x + (a + 1)(a - 1) = 0

➡ x² - (a + 1)x - (a - 1)x + (a + 1)(a - 1) = 0

➡ x[x - (a + 1)] - (a - 1)[x - (a + 1)] = 0

➡ [x - (a - 1)][x - (a + 1)] = 0

➡ (x - a + 1)(x - a - 1) = 0

By zero product rule,

➡ Either (x - a + 1) = 0 or (x - a - 1) = 0

➡ x = a - 1, a + 1

Hence, the values of x are (a - 1) and (a + 1)

Alternative method,

Given,

➡ x² - 2ax + a² - 1 = 0

➡ x² - 2ax + a² = 1

➡ (x)² - 2 × (a) × (x) + (a)² = 1

➡ (x - a)² = 1 [(a - b)² = a² - 2ab + b²]

➡ (x - a) = √1

There are two values of √1, i.e, -1 and 1.

(-1)² = 1 and (1)² = 1

So, when (x - a) = 1

➡ x = a + 1

When (x - a) = -1

➡ x = a - 1

Hence, the values of x are (a + 1) and (a - 1).

Answer:

  • x = a + 1, a - 1
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