Question

33
ab + b + ca = 50, find a + b + C.
34 If a + b - C = 5 and a2 + b2 + c2 = 29, find the value of ab- bc - ca.
35 If a - b = 7 and q2 + b2 = 85. then find the value of a3 - 63.​

Answer 1

Step-by-step explanation:

Answer:

✡ Given ✡

➡ a + b - c = 5

➡ a² + b² + c² = 29

✡ To Find ✡

➡ Value of ab - bc - ca

✡ Solution ✡

Given:-

\leadsto⇝ a + b - c = 5

\leadsto⇝ a² + b² + c² = 29

▶ a + b - c = 5 ( squaring both side we get)

=> (a + b + c)² = (5)²

We know that,

\text{\large\underline{\pink{(a+b+c)² = a²+b²+c²+2ab-2bc-2ca}}}

(a+b+c)² = a²+b²+c²+2ab-2bc-2ca

=> a²+b²+c²+2ab-2bc-2ac = 25

=> (a²+b²+c²) + 2ab - 2bc - 2ac = 25

But,

=> a² + b² + c² = 28 (Given)

=> 29 + 2 (ab-bc-ca) = 25

=> 2 (ab - bc - ca) = -29+25

=> 2 (ab - bc - ca) = -4

=> ab - bc - ca = \dfrac{-4}{2}

2

−4

=> ab - bc - ca = -2

Hence, \bold{\large{\fbox{\color{blue} {ab - bc - ca = -2}}}}

ab - bc - ca = -2