Question

If a+b+c=9 any ab+bc+ca=23
find a²+b²+c²
​

Answer 1

Given:-

• a + b + c = 9 and ab + bc + ca = 23

To Find:-

• a² + b² + c².

IDENTITY USED

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

Now,

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

(9)² = a² + b² + c² + 2(ab + bc + ac)

81 = a² + b² + c² + 2(23)

81 = a² + b² + c² + 46

81 - 46 = a² + b² + c²

35 = a² + b² + c².

Hence ,The Value of a² + b² + c² is 35.

Answer 2

Given:-

a+b+c=9

ab+bc+ca=23

Solution:-

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

⇢ a²+b²+c² + 2×(23) = (9)²

⇢ a²+b²+c² + 46 = 81

⇢ a²+b²+c² = 81-46

⇢ a²+b²+c² = 35

∴ a²+b²+c² = 35