Question

Assertion :If $1\le a\le 2$, then
$\sqrt{a+2\sqrt{a-1}}+\sqrt{a-2\sqrt{a-1}}=2$ Reason: If $1\le a\le 2$, then $(a-1)>1$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

If $1\le a\le 2\Rightarrow 0\le a-1\le 1$

$\Rightarrow \sqrt{a+2\sqrt{a-1}}+\sqrt{a-2\sqrt{a-1}}$

$=\sqrt{1+(a-1)+2\sqrt{a-1}}+\sqrt{1+(a-1)-2\sqrt{a-1}}$
$=\sqrt{1}+\sqrt{a-1}+\sqrt{1}-\sqrt{a-1}=2$
Statement 1 is true. Statement 2 is false.