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# The sum of two numbers a and b is 20. Write an expression for the sum of their squares, in terms of a.

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The sum of two numbers a and b is 20. Write an expression for the sum of their squares, in terms of a.

Sep 28, 2021

#1
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I will start you off.

a+b=20

b=20-a

Sep 28, 2021
#2
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I used your tip and im stuck. I got:

a+b=20

10+10=20

and..

b=20-a

10=20-10

So when it asks "Write an expression for the sum of their squares, in terms of a." I wrote b=20-a and 10=20-10 but the answer still is wrong. Do you know where i was wrong?

Sep 28, 2021
#3
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b=20-a

"Write an expression for the sum of their squares."

a^2+b^2

=

now do the substitution and then simplify.

Melody  Sep 28, 2021
#4
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a^2+b^2 would be 10^2+10^2 which is 100+100 and the answer is 200. Its wrong.

Sep 28, 2021
#5
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a and b are unknown.

you keep saying a=10 and b=10 but that is only one of an infinite number of possibilities.

a could be 8 and b 12

or a could be 5.3 and b could be 14.7

or a could be pi and b could be 20-pi

What you know is that a+b=20    which means   b=20-a

You want the sum of their squares is  a^2 +b^2   but we have to replace b with  20-a

so

\(a^2+b^2\\ =a^2+(20-a)^2\\ =a^2+400+a^2-40a\\ =2a^2-40a+400\)

Melody  Sep 28, 2021
#6
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Oh ok, I understand now. Thank you. Sep 29, 2021
#7
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You are welcome :)

Melody  Sep 29, 2021