Question

If a+b+c =25 anda2+b2+c2=375 find ab+bc+ca

Answer 1

Question

If a+b+c =25 anda2+b2+c2=375 find ab+bc+ca = ?

Solution

Given :-

• a + b + c = 1 ------------(1)
• a² + b² + c² = 375 -----(2)

Find :-

• Value of ( ab + bc + ca)

Explanation

Using Formula

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

So, Now , Squaring both side of equ(1)

➥ ( a + b + c)² = 1²

➥ a² + b² + c² + 2(ab + bc + ca) = 1

Keep Value by equ(2)

➥ 375 + 2(ab + bc + ca) = 1

➥ 2(ab + bc + ca) = 1 - 375

➥ ( ab + bc + ca ) = - 374/2

➥ ( ab + bc + ca ) = - 187

Hence

• Value of ( ab + bc + ca ) = - 187

_________________

Answer 2

$\huge\mathbb\blue{HEY\:USER,}$

$\huge\text{Here is Your answer}$

GIVEN,

$a+b+c=25$

$a^2+b^2+c^2=375$

TO FIND,

$ab+bc+ca$

Now,

$\tt(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)$

Put the values,

$(25)^2=375+2(ab+bc+ac)$

$625=375+2(ab+bc+ac)$

$250=2(ab+bc+ca)$

$\frac{250}{2}=ab+bc+ca$

$ab+bc+ac=125$

$\huge\text{Some of the useful algebraic identities}$

• $(a+b)^2=a^2+b^2+2ab$

• $(a-b)^2=a^2-2ab+b^2$

Hence,

The Value of ab+bc+ac=125.

Thank You!

BeBrainly.