If a + b + c = 9 and ab + bc + ca = 26, find a² + b² + c²
Solution:
Given, a + b + c = 9
Also, ab = bc + ca = 26
We have to find a² + b² + c²
Using the algebraic identity,
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca ---------- (1)
Now, (a + b + c)² = (9)² = 81
Equation (1) can be written as (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
So, 81 = a² + b² + c² + 2(26)
81 = a² + b² + c² + 52
a² + b² + c² = 81 - 52
a² + b² + c² = 29
Therefore, a² + b² + c² = 29
✦ Try This: If a + b + c = 8 and ab + bc + ca = 24, find a² + b² + c²
Given, a + b + c = 8
Also, ab = bc + ca = 24
We have to find a² + b² + c²
Using the algebraic identity,
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca ---------- (1)
Now, (a + b + c)² = (8)² = 64
Equation (1) can be written as (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
So, 64 = a² + b² + c² + 2(24)
64 = a² + b² + c² + 48
a² + b² + c² = 64 - 48
a² + b² + c² = 16
Therefore, a² + b² + c² = 16
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 30
If a + b + c = 9 and ab + bc + ca = 26, find a² + b² + c²
Summary:
If a + b + c = 9 and ab + bc + ca = 26, then a² + b² + c² using the algebraic identity is 29
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