Asked • 03/26/19

If a+b+c+d=10a+b+c+d=10 with c=dc=d and a2+b2+c2+d2=30a2+b2+c2+d2=30where a,b,c,da,b,c,d are positive real numbers, what is the largest possible value of c?

Al P.

From the first condition a+b+c+d = 10a+b+c+d we can immediately conclude a=0. A nit: "positive real numbers" excludes 0. Your teacher should be asking for "nonnegative real numbers" if he or she wants to allow variables to be equal to 0. Get used to precision in mathematics. From c=dc=d, c = d/d = 1.
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03/30/19

David L.

I think the equations should be: a + b + c + d = 10 a^2 + b^2 + c^2 + d^2 = 30 c = d a, b, c, d are positive real numbers
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04/02/19

David L.

a+b+c+d=10; a^2+b^2+c^2+d^2=30; c=d
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04/02/19

Heather P.

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That's how I read it, David. I think there was just too much pasted from the copy/paste. And it looks like there's missing information.
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05/29/19

Patrick B.

The browser tends to duplicate the student input. I have seen a lot of that happening
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06/27/19

1 Expert Answer

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Raymond B. answered • 08/04/19

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the first equality can only be true if a=0. The 2nd means c=d where cd is the same, so c=d=1 or 0

c and d are either both 0 or both 1 If c=d=0 then b^2=30 means b is the square root of 30.

If c=d=1 then b^2 = 30-2=28 and b=the square root of 28.


In either case, the maximum value and only value of c is 1, since they are all positive numbers


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