If a and b are positive, and a+b = 1, then
(a + 1/a)2 + (b + 1/b)2 is
a. ≥ 25/2
b. ≥ 25/4
c. ≤ 25/2
d. ≤ 25/4
So the minimum value is 25/2
take a =1/10 nd b=9/10
(a+1/a)^2 >100!!!!!!!!!!!!!!!!
Sol. We know (a + 1/a)2 + (b + 1/b)2 ≥ 2(a + 1/a)(b + 1/b)
(a + 1/a)2 + (b + 1/b)2 ≥ 2(1 + ab)2 /ab
If a + b = 1, then max. value of ab is 1/4.
(a + 1/a)2 + (b + 1/b)2 ≥ 2(1 + 1/4)2 /(1/4)
(a + 1/a)2 + (b + 1/b)2 ≥ 25/2
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So the minimum value is 25/2
take a =1/10 nd b=9/10
(a+1/a)^2 >100!!!!!!!!!!!!!!!!
take a =1/10 nd b=9/10
(a+1/a)^2 >100!!!!!!!!!!!!!!!!
If a and b are positive, and a+b = 1, then
(a + 1/a)2 + (b + 1/b)2 is
a. ≥ 25/2
b. ≥ 25/4
c. ≤ 25/2
d. ≤ 25/4
Sol. We know (a + 1/a)2 + (b + 1/b)2 ≥ 2(a + 1/a)(b + 1/b)
(a + 1/a)2 + (b + 1/b)2 ≥ 2(1 + ab)2 /ab
If a + b = 1, then max. value of ab is 1/4.
(a + 1/a)2 + (b + 1/b)2 ≥ 2(1 + 1/4)2 /(1/4)
(a + 1/a)2 + (b + 1/b)2 ≥ 25/2
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