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The Value of ($$\sqrt {6} $$ + $$\sqrt {10} $$ - $$\sqrt {21} $$ - $$\sqrt {35} $$) × ($$\sqrt {6} $$ - $$\sqrt {10} $$ + $$\sqrt {21}$$ - $$\sqrt {35} $$) = ?
Answer & Solution
Correct Answer:
Option
D
($$\sqrt {6} $$ + $$\sqrt {10} $$ - $$\sqrt {21} $$ - $$\sqrt {35} $$) × ($$\sqrt {6} $$ - $$\sqrt {10} $$ + $$\sqrt {21} $$ - $$\sqrt {35} $$)
= {($$\sqrt {6} $$ - $$\sqrt {35} $$) + ($$\sqrt {10} $$ - $$\sqrt {21} $$)} × {($$\sqrt {6} $$ - $$\sqrt {35} $$) - ($$\sqrt {10} $$ - $$\sqrt {21} $$)}
= ($$\sqrt {6} $$ - $$\sqrt {35} $$)2 - ($$\sqrt {10} $$ - $$\sqrt {21} $$)2
= 6 + 35 - 2$$\sqrt {210} $$ - 10 - 21 + 2$$\sqrt {210} $$
= 41 - 31
= 10
= {($$\sqrt {6} $$ - $$\sqrt {35} $$) + ($$\sqrt {10} $$ - $$\sqrt {21} $$)} × {($$\sqrt {6} $$ - $$\sqrt {35} $$) - ($$\sqrt {10} $$ - $$\sqrt {21} $$)}
= ($$\sqrt {6} $$ - $$\sqrt {35} $$)2 - ($$\sqrt {10} $$ - $$\sqrt {21} $$)2
= 6 + 35 - 2$$\sqrt {210} $$ - 10 - 21 + 2$$\sqrt {210} $$
= 41 - 31
= 10
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