Question

If a = 2+ √5 and b = 1/a find a^2 + b^2​

Answer 1

• Answer: The Value of: a^2 + b^2 = 18

Hence, The Value of: a^2 + b^2 is 18

• Step-by-step explanation: √

• Find the RECIPROCAL of: a

b = 1/a = 1/ 2 + √5

• Rationalize the Denominator:

b = 1/2 + √5 * 2 - √5/2 - √5

= 2 - √5/1

• Simplify:

b = 2 - √5

• Square: A and B:

a^2 = (2 + √5)^2 = 4 + 4√5 + 5

b^2 = (2 - √5)^2 = 4 - 4√5 + 5

• ADD: a^2 and b^2:

a^2 + b^2 = 4 + 4√5 + 5 + 4 - 4√5 + 5

= 18 - 3√5

• So, Now we solve the Inverse property of addition: ±

4 + 5 + 4 + 5

9 + 4 + 5

13 + 5 = 18

• Move the expression to the right:

a^2 + b^2 = 18

a^2 = 18 - b^2

• Now we take the root of both sides/Negative/Positive:

a = ± √18 - b^2

a = √18 - b^2

a = -√18 - b^2

• Draw a conclusion:

Hence, The Value of: a^2 + b^2 is 18

I hope this helps you!