A very easy problem

Algebra Level 2

We have two numbers a and b if arithmatic mean between a and b is equal to geometric mean between them and value of a is equal to 17 find out the value if b


The answer is 17.

Aman Sharma by Aman Sharma , 25, India

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2 solutions

Arithmetic mean: a + b 2 \frac{a+b}{2} Geometric mean: a b \sqrt{ab} a + b 2 = a b \frac{a+b}{2}=\sqrt{ab} ( a + b 2 ) 2 = a b \left(\frac{a+b}{2}\right)^2=ab a 2 + 2 a b + b 2 4 = a b \frac{a^2+2ab+b^2}{4}=ab a 2 + 2 a b + b 2 = 4 a b a^2+2ab+b^2=4ab a 2 − 2 a b + b 2 = 0 a^2-2ab+b^2=0 ( a − b ) 2 = 0 (a-b)^2=0 a − b = 0 a-b=0 a = b a=b b = a = 17 b=a=\boxed{17}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Jenosha Sarah
Oct 2, 2014

geometric mean will be
sqrt(a.b) ----(1)
arith. mean will be
(a+b)/2 -----(2)
(1)=(2)
sqrt(ab)=(a+b)/2
[sq. both sides]
ab=(a^2+b^2+2ab)/4
4ab=(a^2+b^2+2ab)
0=a^2+b^2-2ab
0=(a-b)^2
0=a-b [sqrt. both sides]
a=b



1 Helpful 0 Interesting 0 Brilliant 0 Confused

therefore b=17

Jenosha Sarah - 6 years, 8 months ago

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