SOLUTION: a^3 - b^2 = 11 a^2 + b = 13

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Question 1206952: a^3 - b^2 = 11
a^2 + b = 13
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E3+-+b%5E2+=+11.....eq.1
a%5E2+%2B+b+=+13....eq.2
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start with
a%5E2+%2B+b+=+13....eq.2, solve for b
b+=+13-a%5E2....eq.1a

go to eq.2, substitute b

+a%5E3+-+%2813-a%5E2%29%5E2+=+11.....eq.1
a%5E3+-+%28a%5E4+-+26+a%5E2+%2B+169%29+=+11
+a%5E3+-+a%5E4+%2B+26+a%5E2+-+169+=+11
a%5E3+-+a%5E4+%2B+26a%5E2+-+169+-11=0
a%5E3+-+a%5E4+%2B+26a%5E2+-+180=0....factor
-%28a+-+3%29+%28a%5E3+%2B+2+a%5E2+-+20+a+-+60%29+=+0

real solutions:
-%28a+-+3%29++=+0=> a=3

%28a%5E3+%2B+2+a%5E2+-+20+a+-+60%29+=+0, using calculator we get a≈4.79
go to
b+=+13-a%5E2....eq.1a, substitute a
b+=+13-3%5E2
b=4

b+=+13-4.79%5E2
b=13-22.9441
b≈-9.94
complex solutions: using calculator
a≈-3.3951+%2B+0.9996i, b≈2.4727+%2B+6.7875i
a≈-3.3951+-+0.9996i, b≈2.4727+-+6.7875i

answer:
a=3,b=4
a≈4.79,b≈-9.94
a≈-3.3951+%2B+0.9996i, b≈2.4727+%2B+6.7875i
a≈-3.3951+-+0.9996i, b≈2.4727+-+6.7875i
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