maths

Find the two numbers whose differences is 8 and the sum of their squares is a minimum

Is 11^(1/2) a rational number???
Pls help

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  1. 1st number --- x
    2nd number -- 8-x

    sum of squares = x^2 + (8-x)^2
    = x^2 + 64 - 16x + x^2
    = 2x^2 - 16x + 64
    d(sum of squares)/dx = 4x - 16
    = 0 for max/min

    4x=16
    x = 4

    the two numbers are both 4

    check:
    for the answer, sum of squares = 16+16 = 32
    let 1st be 3.99, the other 4.01
    sum of squares = 3.99^2 + 4.01^2 = 32.002 which is > 32
    true for any other combination of x and 8-x

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    posted by Reiny
  2. 11^(1/2)
    = √11

    since 11 is not a perfect square,
    11^(1/2) is irrational

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    posted by Reiny

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