39a²-33a-6=0 in quadratis equation pls find the answer
Answers
Answer:
Given, a + b + ab = 8 )
b + c + bc = 15 )
c + a + ca = 35 )
we have to find (a + b + c + abc) = ?
from equation (ii),
b + c + bc = 15
b + c(b + 1) = 15
c = (15 - b)/(b + 1)
put it in equation (iii),
(15 - b)/(b + 1) + a + (15 - b)a/(b+ 1) = 35
(15 - b) + a(b + 1) + (15 - b)a = 35(b + 1)
15 - b + ab + a + 15a - ab = 35b + 35
15 + a - b + 15a = 35b + 35
a - b + 15a - 35b = 35 - 15 = 20
16a - 36b = 20
4a - 9b = 5
4a = 5 + 9b
a = (5 + 9b)/4 )
put equation (iv) in equation (i),
(5 + 9b)/4 + b + (5 + 9b)/4 × b = 8
(5 + 9b) + 4b + 5b + 9b² =8 × 4
18b + 9b² + 5 = 32
9b² + 18b - 27= 0
b² + 2b - 3 = 0
(b + 3)(b - 1) = 0.
b = -3 and 1 but a, b , c are positive numbers
so, b = 1
put equation (iv), a = (5 + 9)/4 = 7/2
c = (15 - b)/(b + 1) = (15 - 1)/(1 + 1) = 7
now, a + b + c + abc = 7/2 + 1 + 7 + 7/2 × 1 × 7
= 7/2 + 8 + 49/2
= 56/2 + 8
=28 + 8 = 36
hence, answer is 36
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