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# minimized problem?

Given that a−b=24. If the product ab is minimized, what is the value of a^2+b^2?

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- JOHNLv 74 weeks agoFavorite Answer
ab = a(a – 24) = a² - 24a

d(ab)/da = 2a – 24

d²(ab)/da² = 2 > 0

so ab has a minimum at 2a – 24 = 0 or at a = 12

a – b = 24 → b = a – 24 = 12 -24 = -12.

a² + b² = 12² + (-12)² = 144 + 144 = 288.

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- KrishnamurthyLv 74 weeks ago
Given that a − b = 24.

If the product ab is minimized,

the value of a^2 + b^2 = 626.

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- 4 weeks ago
a * b =>

a * (24 + a)

24a + a^2

P = 24a + a^2

dP/da = 24 + 2a

dP/da = 0

0 = 24 + 2a

0 = 12 + a

a = -12

a - b = 24

-12 - b = 24

-12 - 24 = b

-36 = b

a^2 + b^2 =>

(-12)^2 + (-36)^2 =>

144 + 9 * 144 =>

10 * 144 =>

1440

- atsuoLv 64 weeks agoReport
You said b = 24+a , but if so then b-a = 24 . The question said a-b = 24 .

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