Which of the following is the value of

Question:

Which of the following is the value of $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7}) ?$

(a) $-4$

(b) 4

(c) $\sqrt{11}$

(d) $\sqrt{7}$

 

Solution:

$(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$

$=(\sqrt{11})^{2}-(\sqrt{7})^{2} \quad\left[(a-b)(a+b)=a^{2}-b^{2}\right]$

$=11-7$

$=4$

Hence, the correct answer is option (b).

 

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