If a = √(7) - √(4) , and b = √(14) + √(2) , then which of the following is true?

If a = √(7) - √(4) , and b = √(14) + √(2) , then which of…

If a = $\sqrt{7} - \sqrt{4}$ , and b = $\sqrt{14} + \sqrt{2}$ , then which of the following is true?

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Correct answer: B

Explanation

The correct answer is option 2 i.e. a < b.

a = √7 - √4 and b = √14 + √2

a = √7 - √4 = √7 - 2

⇒ a² = (√7 - 2)² = 11 − 4√7

Also, b² = (√14 + √2)² = 16 + 4√7

b² - a² = (16 + 4√7) - (11 - 4√7) = 5 + 8√7

Since 8√7 is positive, b² > a² ⇒ b > a ⇒ a < b