Question

if a+b+c=9 and ab +bc+can=40 find a square b square and c square​

Answer 1

Answer:

Hi there !!Given,a + b + c = 9ab + bc + ca = 40To find : a² + b² + c²The following expression matches to the algebraic identity (a + b + c)² = a² + b² + c² + 2a…....

Answer 2

$\red\bigstar$ Correct Question:

• If a + b + c = 9 and ab + bc + ca = 40. Then find a² + b² + c².

$\red\bigstar$Answer:

• a² + b² + c² = 1

$\red\bigstar$Given:

• a + b + c = 9
• ab + bc + ca = 40

$\red\bigstar$To find:

• a² + b² + c²

$\red\bigstar$ Solution:

We know that,

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

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

Now, by substituting the values of ( a + b + c ) and ab + bc + ca, we get:

( 9 )² = a² + b² + c² + 2( 40)

( $\because$ a + b + c = 9 and ab + bc + ca = 40)

$\implies$ 81 = a² + b² + c² + 80

$\implies$ a² + b² + c² + 80 = 81

$\implies$ a² + b² + c² = 81 - 80

$\implies$$\boxed{a² \:+ \:b²\: +\: c²\: =\:1}$

$\therefore$a² + b² + c² = 1