Question

If a + b + c = 9 and ab + bc + ac = 40, then find the value for : a^2 + b^2 + c^2​

Answer 1

Answer:

1

Step-by-step explanation:

(a+b+c)² = a²+b²+c²+2ab+2bc+2ca

9² = a²+b²+c²+2(ab+bc+ca)

81 = a²+b²+c²+2×40

a²+b²+c² = 81-80

= 1

Answer 2

Given :-

• a + b + c = 9

•ab + bc + ac = 40

To Find :-

• value of a² + b² + c²

Formula to be used :-

• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Solution :-

We know,

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

⟼ (a² + b² + c²) = (a + b + c)² - 2(ab + bc + ca)

Now, put the given values in the formula to get the value of a² + b² + c².

⟼a² + b² + c² = 9² - 2(40)

⟼ a² + b² + c² = 81 - 80

⟼ a² + b² + c² = 1

Hence,

$Value \: \: of \: a² + b² + c² \: \: is  \: = 1$

Extra Information :-

•Some identities :-

1. (a + b)² = a² + 2ab + b²

2. (a – b)² = a² – 2ab + b²

3. (x + a)(x + b) = x² + (a + b)x + ab

4. (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

5. a³ – b³ = (a – b)(a² + ab + b²)

6. (a + b)³ = a³ + 3a²b + 3ab² + b³

7. (a – b)³ = a³ – 3a²b + 3ab² – b³

8.a³ + b³ = (a + b)(a² – ab + b²)