If a , b , c are distinct positive real in H.P., then the value of the expression, ( b + a / b - a )+( b + c / b - c ) is equal to

Question

If a , b , c are distinct positive real in H.P., then the value of the expression, ( b + a / b - a )+( b + c / b - c ) is equal to (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

E =( b + a / b - a )+( b + c / b - c ), b =(2 ac / a + c )( b 2 ≠ ac ) E =((b2-b c+a b-a c)+(b2+b c-a b-a c)/(b-a)(b-c))=(2(b2-a c)/b2-b c-a b+a c)=(2(b2-a c)/b2-b(a+c)+a c) =(2(b2-a c)/b2-2 a c+a c)=2

Q. If a,b,c are distinct positive real in H.P., then the value of the expression, b−ab+a​+b−cb+c​ is equal to

1

2

3

4

E=b−ab+a​+b−cb+c​,b=a+c2ac​(b2=ac) E=(b−a)(b−c)(b2−bc+ab−ac)+(b2+bc−ab−ac)​=b2−bc−ab+ac2(b2−ac)​=b2−b(a+c)+ac2(b2−ac)​ =b2−2ac+ac2(b2−ac)​=2

Q. If $a, b, c$ are distinct positive real in H.P., then the value of the expression, $\frac{b + a}{b - a} + \frac{b + c}{b - c}$ is equal to