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InterviewSolution
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If \(\sqrt{11 - 3 \sqrt{8}} = a + b \sqrt{2}\), then what is the value of (2a + 3b)?1. 72. 93. 34. 5 |
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Answer» Correct Answer - Option 3 : 3 Concept used: (a – b)2 = a2 – 2ab + b2 Calculations: \(\sqrt{11 - 3 \sqrt{8}} = a + b \sqrt{2}\) \(⇒ \sqrt{11 - 3 \sqrt{2 × 2 × 2}} = a + b \sqrt{2}\) \(⇒ \sqrt{11 - 2 × 3 \sqrt{2}} = a + b \sqrt{2}\) \(⇒ \sqrt{(3)^2 + (\sqrt2)^2 - 2 × 3 \sqrt{2}} = a + b \sqrt{2}\) \(⇒ \sqrt{(3\;-\;√2)^2} = a + b \sqrt{2}\) ⇒ 3 – √2 = a + b√2 Compare a and b ⇒ a = 3 ⇒ b = -1 Value of (2a + 3b) = 2 × 3 + 3 × (-1) ⇒ 6 – 3 = 3 ∴ Value of 2a + 3b is 3 |
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