Question

if a+b+c=12 and a² + b²+ c²= 50, find ab+
bc+ ca
Select from the Answers below

O 97 0 62
O 47 O 38​

Answer 1

Answer:

94

None of the answer is right check the options again

hope it helps you

Answer 2

Analysis→

Here we're given that a+b+c=12 and a²+b²+c²=50. And we've to find the value of ab+bc+ca. And according to the Identity: (x+y+z)²=x²+y²+z²+2(xy+yz+zx) And by substituting the variables and putting the values given, we can easy find the answer.

Options Given→

1. 97
2. 47
3. 62
4. 38

Given→

• a+b+c=12
• a²+b²+c²=50

To Find→

The value of ab+bc+ca.

Answer→

$\large{\underline{\boxed{\rm{Using\:Identity:\big(x+y+z\big)^2=x^2+y^2+z^2+2\big(xy+yz+zx\big)}}}}$

$\rm{ \big(x+y+z\big)^2=x^2+y^2+z^2+2\big(xy+yz+zx\big)}$

$\rm{ \big(a+b+c\big)^2=a^2+b^2+c^2+2\big(ab+bc+ca\big)}$

$\rm{ \big(12\big)^2=\big(50\big)+2\big(ab+bc+ca\big)}$

$\implies\rm{ 144=50+2\big(ab+bc+ca\big)}$

$\implies\rm{ 2\big(ab+bc+ca\big)=94}$

$\implies\rm{ \big(ab+bc+ca\big)=\dfrac{94}{2}}$

$\implies\rm{ \big(ab+bc+ca\big)=\dfrac{\cancel{94}}{\cancel{2}}}$

$\implies\rm{ \big(ab+bc+ca\big)=47}$

${\boxed{\boxed{\implies{\bf{ \big(ab+bc+ca\big)=47\checkmark}}}}}$

☞ Hence the value of ab+bc+ca is 47, therefore option (2) is the correct answer.

Know More→

Some more algebraic identities:-

1. (x+y)²=x²+y²+2xy
2. (x-y)²=x²+y²-2xy
3. x²-y²=(x+y)(x-y)
4. (x+a)(x+b)=x²+x(a+b)+ab
5. (x+b)³=x³+y³+3xy(x+y)
6. (x-y)³=x³-y³-3xy(x-y)
7. x³+y³=(x+y)(x²+y²-xy)
8. x³-y³=(x-y)(x²+y²+xy)
9. x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-zx)

HOPE IT HELPS.