Question

A✓a + b✓b = 32 and a✓b + b✓a = 31. what is 5ge value of 5(a+b)/7

Answer 1

Answer:

5(a+b)/7 = 9

Step-by-step explanation:

Let a = x² & b = y²

a✓a + b✓b = 32

∴ x³ + y³ = 32--- eqn 1

a✓b + b✓a = 31

∴ x²y + xy² = 31  --- eqn 2

Multiplying by 3, we get

3x²y + 3xy² = 93 --- eqn 3

Adding eqn 1 & 3

x³ + y³ + 3x²y + 3xy² = 32+93

(x+y)³ = 125

x+y = 5 --- eqn 4

Simplifying eqn 2,  x²y + xy² = 31

xy(x+y) = 31

5xy = 31

xy = 31/5 --- eqn 4

Now (a+b)= x²+ y² = (x+y)² - 2xy

(a+b)= 5² - 2×31/5 = 25-62/5=(125-62)/5

∴ (a+b) = (63/5)

∴ 5(a+b)/7 = (5×63/5) /7

=63/7 = 9

5(a+b)/7 = 9