Question

7a^2+7b^2+7c^2-7ab-7bc-7ca=0 find the value of a+b/c+a​

Answer 1

Answer:

answer is (C /B )

Step-by-step explanation:

as seen above u can put the value of ab +BC +ca =0 andur question will get solved

Answer 2

Answer:

The value of  $\frac{a+b}{c+a}$ = 1

Step-by-step explanation:

Given,

7a²+7b²+7c²-7ab-7bc-7ca=0

To find,

The value of  $\frac{a+b}{c+a}$

Solution:

7a²+7b²+7c²-7ab-7bc-7ca=0

⇒7(a²+b²+c²-ab-bc-ca)=0

⇒a²+b²+c²-ab-bc-ca=0

⇒$\frac{1}{2}$[2a²+2b²+2c²-2ab-2bc-2ca]=0

⇒2a²+2b²+2c²-2ab-2bc-2ca=0

⇒(a²+b² -2ab)+(b² +c²-2bc) +(a² +c²-2ca)=0

Applying the identity (a-b)² = a²+b² -2ab we get,

⇒(a-b)²+(b-c)² +(a-c)²=0

⇒(a-b)²= 0, (b-c)² = 0, (a-c)²=0

⇒a-b= 0, b-c = 0, a-c=0

⇒a = b, b = c , a = c

⇒a = b = c -------------------------(1)

$\frac{a+b}{c+a}$ = $\frac{a+a}{a+a}$ (by substituting the value of b and c as 'a' from equation (1) we get

= $\frac{2a}{2a}$ = 1

∴ $\frac{a+b}{c+a}$ = 1

The value of  $\frac{a+b}{c+a}$ = 1

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