Question

If p + q = 10 and pq = 5 then find the value of p/q + q/p

• A. 22
• B. 20
• C. 18
• D. 16

Answer 1

Answer:

C. 18

• The expression becomes: (p × p) / (q × p) + (q × q) / (p × q) = (p² + q²) / pq.

• We are given p + q = 10 and pq = 5.

• Find p² + q²:. Recall the algebraic identity for squaring a binomial: (a + b)² = a² + b² + 2ab.

• Applying this to our problem: (p + q)² = p² + q² + 2pq.

• We want to find p² + q², so rearrange the identity: p² + q² = (p + q)² - 2pq.

• Now, substitute the given values: p² + q² = (10)² - 2(5).

• Calculate the values: p² + q² = 100 - 10 = 90.

• Substitute Back into the Simplified Expression: Now we have all the components for (p² + q²) / pq.

• Substitute the calculated values: 90 / 5.

• Perform the division: 90 / 5 = 18.