Question

a+b+c=20, ab+BC+ca=150, find value of a^2+b^2+c^2

Answer 1

Answer:

100

Step-by-step explanation:

Given-----> a + b + c = 20 , ab + bc + ca = 150

To find-----> a² + b² + c² = ?

Solution-----> ATQ,

a + b + c = 20 , ab + bc + ca = 150

We know that ,

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

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

Putting ( a + b + c ) = 20 and ab + bc + ca = 150 , in it , we get,

=> ( 20 )² = ( a² + b² + c² ) + 2 ( 150 )

=> 400 = ( a² + b² + c² ) + 300

=> 400 - 300 = ( a² + b² + c² )

=> 100 = ( a² + b² + c² )

=> a² + b² + c² = 100

Additional information ------>

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

3) ( a + b )³ = a³ + b³ + 3ab ( a + b )

4) ( a - b )³ = a³ - b³ - 3ab ( a - b )

5) ( a³ - b³ ) = ( a - b ) ( a² + b² + ab )

6) ( a³ + b³ ) = ( a + b ) ( a² + b² - ab )

7) ( a² - b² ) = ( a + b ) ( a - b )

Answer 2

Question a+b+c=20, ab+BC+ca=150, find value of a^2+b^2+c^2

Solution

Given : 1) a+b+c=20

2) ab+bc+ca

To find : value of

${a}^{2} + {b}^{2} + {c}^{2}$

I d e n t I t y u s e d :

$(a + b + c) {}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ substituting \: the \: value \: as \: given \: in \: the \: question \: \\ 20 {}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ taking \: 2 \: as \: common \\ {20}^{2} = {a}^{2} + {b}^{2} + {c}^{2} \: + 2(150) \\ {20}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 300 \\ 400 = {a}^{2} + {b}^{2} + {c}^{2} + 300 \\ 400 - 300 = {a}^{2} + {b}^{2} + {c}^{2} \\ 100 = {a}^{2} + {b}^{2} + {c}^{2}$

hence we got

{a}^{2} + {b}^{2} + {c}^{2} = 100

Thanks