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If a=(1+0.5^1/2)/(1-0.5^1/2) and b=(1-0.5^1/2)/(1+0.5^1/2)
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03 Nov 2024, 09:06
03 Nov 2024, 09:06
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If \(a= \frac{(1+\sqrt{0.5})}{(1-\sqrt{0.5})}\) and \(b= \frac{(1-\sqrt{0.5})}{(1+\sqrt{0.5})}\)
Then find \( \frac{(a^2 + b^2 + ab)}{35}\)
A. \(6\)
B. \(\frac{6}{35}\)
C. \(5\)
D. \(1\)
don’t hesitate to mention me if ya need official keys. edited to have nicer numbers in options, others told me that previous one was not tricky enough to make careless person fall in trap and choose the incorrect one
Then find \( \frac{(a^2 + b^2 + ab)}{35}\)
A. \(6\)
B. \(\frac{6}{35}\)
C. \(5\)
D. \(1\)
don’t hesitate to mention me if ya need official keys. edited to have nicer numbers in options, others told me that previous one was not tricky enough to make careless person fall in trap and choose the incorrect one
If a=(1+0.5^1/2)/(1-0.5^1/2) and b=(1-0.5^1/2)/(1+0.5^1/2)
[#permalink]
05 Nov 2024, 23:07
05 Nov 2024, 23:07
1
(a) \(a^2+b^2+ab= a^2+b^2+ab+(ab-ab)\)
(b) \((a+b)^2+(a-b)^2=2(a^2+b^2)\)
From (a) we have equation \(\frac{(a+b)^2-ab}{35}\)
From (b):
(1): ab = \(\frac{(1+\sqrt{0.5})}{(1-\sqrt{0.5})}*\frac{(1-\sqrt{0.5})}{(1+\sqrt{0.5})}\)= 1
(2): (a+b) = \(\frac{(1+\sqrt{0.5})^2+(1-\sqrt{0.5})^2}{(1-0.5)}=\frac{2(1.5)}{0.5}\)= 6
Combine (1),(2): \(\frac{6^2-1}{35}\)=1
thanks your kudos (/ >3<)/
(b) \((a+b)^2+(a-b)^2=2(a^2+b^2)\)
From (a) we have equation \(\frac{(a+b)^2-ab}{35}\)
From (b):
(1): ab = \(\frac{(1+\sqrt{0.5})}{(1-\sqrt{0.5})}*\frac{(1-\sqrt{0.5})}{(1+\sqrt{0.5})}\)= 1
(2): (a+b) = \(\frac{(1+\sqrt{0.5})^2+(1-\sqrt{0.5})^2}{(1-0.5)}=\frac{2(1.5)}{0.5}\)= 6
Combine (1),(2): \(\frac{6^2-1}{35}\)=1
thanks your kudos (/ >3<)/
gmatclubot
If a=(1+0.5^1/2)/(1-0.5^1/2) and b=(1-0.5^1/2)/(1+0.5^1/2) [#permalink]
05 Nov 2024, 23:07
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