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If a= 3-root 5 ÷ 3+root 5 and b= 3+root 5÷3- root 5 find a^2-b^2?
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If a= 3-root 5 ÷ 3+root 5 and b= 3+root 5÷3- root 5 find a^2-b^2?
Solution:

Step 1: Simplify a and b

We have:

a = 3 - √5 ÷ 3√5

b = 3√5 ÷ 3 - √5

Let's simplify a and b one by one:

a = (3 - √5) ÷ (3√5)

Multiplying both numerator and denominator by (3 + √5), we get:

a = (3 - √5) ÷ (3√5) x (3 + √5) ÷ (3 + √5)

a = (9 + 3√5 - 3√5 - 5) ÷ (9 - 5)

a = 4 ÷ 4

a = 1

Similarly, let's simplify b:

b = 3√5 ÷ 3 - √5

Multiplying both numerator and denominator by (3 + √5), we get:

b = 3√5 ÷ 3 - √5 x (3 + √5) ÷ (3 + √5)

b = (9√5 + 3√5√5 - 3√5 - 5) ÷ (9 - 5)

b = (6√5) ÷ 4

b = (3√5) ÷ 2


Step 2: Evaluate a^2 - b^2

Now, we need to evaluate a^2 - b^2:

a^2 - b^2 = (1)^2 - ((3√5 ÷ 2)^2)

a^2 - b^2 = 1 - 9 ÷ 4

a^2 - b^2 = -5 ÷ 4


Step 3: Conclusion

Therefore, a^2 - b^2 = -5 ÷ 4.
Community Answer
If a= 3-root 5 ÷ 3+root 5 and b= 3+root 5÷3- root 5 find a^2-b^2?
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