Math, asked by vkpatel63, 1 year ago

Find the value of a + b + c, if 900 =(abc)​

Answers

Answered by abhi178
0

minimum value of a + b + c = 3(30)⅓

but minimum integral value of a + b + c = 10

question is -> find the minimum value of a + b + c , if 900 = (abc)² , where a , b , c ∈ R+

using application,

arithmetic mean, AM ≥ geometric mean, GM

⇒arithrmetic mean of a, b and c = (a + b + c)/3

geometric mean of a , b and c = (abc)⅓

now, (a + b + c)/3 ≥ (abc)⅓

[ given, 900 = (abc)² ⇒ 30 = (abc)

⇒(a + b + c)/3 ≥ (30)⅓

⇒(a + b + c) ≥ 3(30)⅓

so, the minimum value of a + b + c = 3(30)⅓

if you want minimum integral value of a + b + c , then a + b + c = 10

also read similar questions: Is 900 a perfect square? If so, find the number whose square is 900.

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