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प्रश्न
Find the smallest possible value of x2 + y2 given that x + y = 10
उत्तर
Given x + y = 10
⇒ y = 10 – x
Let A = x2 + y2
A = x2 + (10 – x)2
`"dA"/("d"x)` = 2x + 2(10 – x)(– 1)
For maximum or minimum,
`"dA"/("d"x)` = 0
⇒ 2(2x – 10) = 0
x = 5
`("d"^2"A")/("d"x^2)` = 4
At x = `5, ("d"^2"A")/("d"x^2) > 0`
∴ A is minimum when x = 5
y = 10 – 5
= 5
∴ The smallest possible value of x2 + y2 is
= (5)2 + (5)2
= 25 + 25
= 50
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