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03 Jul 2024, 01:25
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:50) correct
34%
(02:20)
wrong
based on 165
sessions
History
Date
Time
Result
Not Attempted Yet
If \((\sqrt{2} + \sqrt{3})^{1000} = x\), what is the value of \((\sqrt{2}-\sqrt{3})^{1000}\), in terms of \(x\)?
A. \(x^2\)
B. \(2x\)
C. \(3x\)
D. \(\frac{1}{x}\)
E. \(-x\)
A. \(x^2\)
B. \(2x\)
C. \(3x\)
D. \(\frac{1}{x}\)
E. \(-x\)
03 Jul 2024, 01:50
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sahilsah456
\((\sqrt{2}-\sqrt{3})^{1000}=\)
\(=(\frac{(\sqrt{2}-\sqrt{3})(\sqrt{2} + \sqrt{3})}{\sqrt{2} + \sqrt{3}})^{1000}=\)
\(=(\frac{(\sqrt{2})^2-(\sqrt{3})^2}{\sqrt{2} + \sqrt{3}})^{1000}=\)
\(=(\frac{-1}{\sqrt{2} + \sqrt{3}})^{1000}=\)
\(=\frac{(-1)^{1000}}{(\sqrt{2} + \sqrt{3})^{1000}}=\)
\(=\frac{1}{x}\)
03 Jul 2024, 02:15
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sahilsah456
I think I have much simpler explanation
\((\sqrt{2} + \sqrt{3})^{1000} = x\) i.e. x is (1.4+1.7)^1000
\((\sqrt{2}-\sqrt{3})^{1000}\) is (1.4-1.7)^1000 i.e. .3^1000 (Very small but positive number
A. \(x^2\) it's much bigger than x so NOT POSSIBLE
B. \(2x\) it's much bigger than x so NOT POSSIBLE
C. \(3x\) it's much bigger than x so NOT POSSIBLE
D. \(\frac{1}{x}\) much smaller than x so POSSIBLE
E. \(-x\) Negative hence NOT POSSIBLE
Answer: Option D
