Math, asked by sorenshania38, 3 months ago

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​

Answers

Answered by aditi2944
2

Answer:

94

None of the answer is right check the options again

hope it helps you

Attachments:
Answered by gotoo000612y
51

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.

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