Question

$\huge\red{QuesTiON}$

$if (a+b+c)^2=32;ab+bc+ca=10 then a^2+b^2+c^2=??$


report my previous 2 QuesTiONs​

Answer 1

Given that:

(a + b + c)² = 32

ab + bc + ca = 10

To find:

a² + b² + c²

Solution:

ATQ:

$\sf \Longrightarrow (a + b + c)^2 = 32$

| We know that:

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

$\sf \Longrightarrow a^2 + b^2 + c^2 + 2ab + 2bc + 2ac = 32$

Taking 2 as a common term from 2ab, 2bc & 2ac we get:

$\sf \Longrightarrow a^2 + b^2 + c^2 + 2(ab + bc + ac) = 32$

| ATQ:

| ab + bc + ca = 10

| Substitute this value above.

$\sf \Longrightarrow a^2 + b^2 + c^2 + 2(10) = 32$

$\sf \Longrightarrow a^2 + b^2 + c^2 + 20 = 32$

$\sf \Longrightarrow a^2 + b^2 + c^2 = 32 - 20$

$\sf \Longrightarrow a^2 + b^2 + c^2 = 12$

Final answer: 12

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Some other useful identities:

• (a + b)² = a² + b² + 2ab

• (a - b)² = a² + b² - 2ab

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ - b³ - 3ab(a - b)

• a³ + b³ = (a + b)³ - 3ab(a + b)

• a³ - b³ = (a - b)³ + 3ab(a - b)

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

Answer 2

Step-by-step explanation:

12 is the right answer

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