Question:
Simplify the expression: \(\dfrac{(\sqrt{7}+\sqrt{3})^2 – (\sqrt{7}-\sqrt{3})^2}{\sqrt{7} \times \sqrt{3}}\)
व्यंजक को सरल कीजिए: \(\dfrac{(\sqrt{7}+\sqrt{3})^2 – (\sqrt{7}-\sqrt{3})^2}{\sqrt{7} \times \sqrt{3}}\)
Options:
- 2
- 4
- 6
- 8
- 2
- 4
- 6
- 8
Correct Answer: b)
Explanation:
Using the identity \((a + b)^2 – (a – b)^2 = 4ab\):
Numerator = \(4 \times \sqrt{7} \times \sqrt{3}\).
Denominator = \(\sqrt{7} \times \sqrt{3}\).
Result = \(\dfrac{4\sqrt{21}}{\sqrt{21}} = 4\).
सर्वसमिका \((a + b)^2 – (a – b)^2 = 4ab\) का प्रयोग करने पर:
अंश = \(4\sqrt{7}\sqrt{3}\), हर = \(\sqrt{7}\sqrt{3}\)। अतः परिणाम = 4।