Answer:
17 and 22yrs
Step-by-step explanation:
Given parameters:
Let Ben's age = B
Let Ima's age = L
B = L + 5 -----i
Also,
the square of their age is 773;
B² + L² = 773 ---ii
To find their ages, substitute equation i into ii;
(L + 5)² + L² = 773
L² + 10L + 25 + L² = 773
2L² + 10L + 25 = 773
2L² + 10L + 25 - 773 = 0
2L² + 10L -748 = 0
Divide through by 2;
L² + 5L - 374 = 0
L² + 22L - 17L - 374 = 0
L(L + 22) - 17(L + 22) = 0
(L - 17)(L + 22) = 0
L = 17 or -22
Age cannot be -22;
Ima's age = 17
Ben's age;
B = L + 5
B = 17 + 5 = 22
