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23 Jun 2020, 10:11
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C
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Difficulty:
45%
(medium)
Question Stats:
68% (02:08) correct
32%
(02:40)
wrong
based on 266
sessions
History
Date
Time
Result
Not Attempted Yet
If \(a > b\) and \(a^2 + b^2 = 4ab\), what is the value of \(\frac{a + b}{a - b}\)?
A. 1
B. \(\sqrt{2}\)
C. \(\sqrt{3}\)
D. 2
E. \(\sqrt{5}\)
A. 1
B. \(\sqrt{2}\)
C. \(\sqrt{3}\)
D. 2
E. \(\sqrt{5}\)
a^2 + b^2 =4ab, a>b. (a+b)/(a-b)=?
23 Jun 2020, 11:04
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Explanation:
a^2+b^2=4ab (Given)
adding Side 2ab
a^2 + b^2 +2ab = 6ab
(a+b)^2 = 6ab
(a+b)= √6ab ---- 1
a^2 + b^2 = 4ab
a^2 + b^2 - 2ab = 2ab
(a-b)^2 = 2ab
(a-b) = √2ab --- 2
From 1 and 2
Required: (a+b)/(a-b) = √6ab / √2ab
= √3
IMO-C
a^2+b^2=4ab (Given)
adding Side 2ab
a^2 + b^2 +2ab = 6ab
(a+b)^2 = 6ab
(a+b)= √6ab ---- 1
a^2 + b^2 = 4ab
a^2 + b^2 - 2ab = 2ab
(a-b)^2 = 2ab
(a-b) = √2ab --- 2
From 1 and 2
Required: (a+b)/(a-b) = √6ab / √2ab
= √3
IMO-C
02 Jul 2020, 13:08
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\(a^2+b^2=4ab\)
\(a^2+b^2+2ab=6ab\)
\((a+b)^2=6ab\)
\(a+b=\sqrt{6ab}\)
\(a^2+b^2=4ab\)
\(a^2+b^2-2ab=2ab\)
\((a-b)^2=2ab\)
\(a-b=\sqrt{2ab}\)
\(\frac{a+b}{a-b}=\frac{\sqrt{6ab}}{\sqrt{2ab}}\)
\(\frac{a+b}{a-b}=\sqrt{3}\)
\(a^2+b^2+2ab=6ab\)
\((a+b)^2=6ab\)
\(a+b=\sqrt{6ab}\)
\(a^2+b^2=4ab\)
\(a^2+b^2-2ab=2ab\)
\((a-b)^2=2ab\)
\(a-b=\sqrt{2ab}\)
\(\frac{a+b}{a-b}=\frac{\sqrt{6ab}}{\sqrt{2ab}}\)
\(\frac{a+b}{a-b}=\sqrt{3}\)
