Question

if a + b - c = 5 and a2 + b2 + c2 = 29 find the value of ab - bc - ca​

Answer 1

Solution

Given :-

• a + b - c = 5 _______(1)
• a² + b² + c² = 29 _____(2)

Find :-

• Value of ab - bc - ca

Explanation

Using Formula

★ (a+b-c)² = a²+b²+c²+2(ab-bc-ca)

Keep all values by equ(1) & equ(2)

➡ (5)² = 29 + 2(ab - bc - ca)

➡25 = 29 + 2(ab - bc - ca)

➡ 25 - 29 = 2(ab - bc - ca)

➡ -4 = 2(ab - bc - ca)

➡ (ab - bc - ca) = -4/2

➡ (ab - bc - ca) = -2

Hence

• Value of (ab - bc - ca) be = -2

_________________

Answer 2

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,

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

=> 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 = $\dfrac{-4}{2}$

=> ab - bc - ca = -2

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