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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