if a+b=5 and a-b=2,what is the value of a^2+b^2?
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answer ; (a+b)^2=a^2+b^2+2ab
a^2+b^2=(a+b)^2-2ab
5^2-2(2)
25-4=21
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a + b = 5 eq.1
a - b = 2 eq.2
By eq.1
a = 5 - b eq.3
Putting eq.3 in eq.2
5 - b - b = 2
- 2b = 2 - 5
- 2b = - 3
2b = 3
b = 3/2
Putting b = 3/2 in eq.3
a = 5 - 3/2
a = (10 - 3)/2
a = 7/2
a^2 = (7/2)^2
a^2 = 49/4
b^2 = (3/2)^2
b^2 = 9/4
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