Question

the sum of two number is 8 find the minumum value of the sum of their squares.
a.32
b.16
c.64
d.24

Answer 1

64-4=60
ans =60
think so

Answer 2

Let's call the numbers a and b, and the sum of their squares S:
a+b=8
Now get b in terms of a, since we'll need that:
b = 8-a
\[S = a ^{2}+b ^{2}\]

now replace b with (8-a)

\[S = a ^{2}+(8-a)^{2}\]

Answer 3

@agent0smith apply maxima minima

Answer 4

i think the answer is 32 what do you think guys?

Answer 5

To find the minimum value of the sum of their squares, we need to differentiate S w.r.t a:
\[S= 2a+2(8-a)(-1)\]

And set that equal to zero, find a, and substitute back into the S equation.

Answer 6

yes the same thing

Answer 7

oh no it is 56
may be m nt sure

Answer 8

Oh and the S in my last reply should be S' not just S.

And yep, the answer is 32. You'll find a=4 from the S' = 0 equation, then you put that a value into the equation for S.

Answer 9

bingo !

Answer 10

u can even apply
AM GM enequality

Answer 11

You can construct the equation.

y = 8- x

We can then construct another for the sum of the squares.

z = y^2 + x^2

Replace y with x or x with y (whichever you prefer).

z = (8-x)^2 + x^2

Then use differentiation to find the minimum point of the curve.

Answer 12

it 32 for sure

Answer 13

^yep, exactly Stephanie.

Answer 14

thank u guys

Answer 15

i just checked it.....if you want me to prove??

Answer 16

no what im
saying is
u can even apply
AM GM enequality