Question

A²+ b² = 20
2a+b=3
A= ? b=?

Answer 1

(a, b) = ((6 +√91)/5, (3 -2√91)/5) ≈ (3.108, -3.216)

(a, b) = ((6 -√91)/5, (3 +2√91)/5) ≈ (-0.708, 4.416)

Explanation:

You want the values of 'a' and 'b' that satisfy the equations ...

• a² +b² = 20
• 2a +b = 3

Solution

The second equation gives an expression for b:

b = 3 -2a

This can be used in the first equation:

a² +(3 -2a)² = 20

a² +9 -12a +4a² = 20

5a² -12a = 11

a² -2.4a = 2.2

(a -1.2)² = 3.64

a = 1.2 ±√3.64 = (6 ±√91)/5

The corresponding values of b are ...

b = 3 -2a = 3 -2(6 ±√91)/5 = (3 ∓2√91)/5

The solutions are ...

(a, b) = ((6 +√91)/5, (3 -2√91)/5) ≈ (3.108, -3.216)

(a, b) = ((6 -√91)/5, (3 +2√91)/5) ≈ (-0.708, 4.416)

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Additional comment

The first attachment shows the decimal values of the answers to calculator precision. The second attachment shows the graphs of the two equations, and their points of intersection.

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