Question

given a+b+c=9 and ab+bc+ca=26 find a^2+b^2+c^2=29​

Answer 1

Step-by-step explanation:

Given:'

${:}\longrightarrow$ $a+b+c=9$

${:}\longrightarrow$$ab+bc+ca=26$

${:}\longrightarrow$ ${a}^{2}+{b}^{2}+{c}^{2}=29$

Solution:-

a+b+c=9

${:}\longrightarrow$${a+b+c}^{2}={9 }^{2}$

${:}\longrightarrow$${a}^{2}+{b}^{2}+{c}^{2}+2ab+2bc+2ca=81$

${:}\longrightarrow$$29+2(ab+bc+ca=81$

${:}\longrightarrow$$29+2 (26)=81$

${:}\longrightarrow$$29+52=81$

${:}\longrightarrow$${a}^{2}+{b}^{2}+{c}^{2}+52=81$

${:}\longrightarrow$${a}^{2}+{b}^{2}+{c}^{2}=81-52$

${:}\longrightarrow$${\underline{\boxed {\sf{{a}^{2}+{b}^{2}+{c}^{2}=29}}}}$

Hence verified

Extra information:-

used formula:-

${a+b+c}^{2}={a}^{2}+{b}^{2}+{c}^{2}+2ab+2bc+2ca$

Answer 2

Answer:

29.

Step-by-step explanation:

a + b + c = 9

Squaring on both the sides,

(a + b + c)² = (9)²

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

a² + b² + c² + 2(ab + bc + ca) = 81

Substituting ab + bc + ca = 26 in the equation,

a² + b² + c² + 2(26) = 81

a² + b² + c² = 81 - 52

Thus, a² + b² + c² = 29

Hope this helps you :)