Question

Express linear equation 2x + 3y is equal to 5 in the form of ax + by + c is equal to zero and indicate values of a b and c ​

Answer 1

Answer:

Step-by-step explanation:

2x+3y=5

2x+3y-5=0 in the form of ax+by+c

a     b   c

a=2,b=3,c=-5

Answer 2

Answer:If a+b+c=0 , what's the value of (ab−c+bc−a+ca−b)(b−ca+c−ab+a−bc) ?

There are too many variables for my taste and I think the prime concern is to proceed avoiding as much algebra as possible. Since the expressions are both cyclic, let b=sa and c= ta . The condition becomes 1+s+t=0. The expression becomes

E=(1s−t+st−1+t1−s)(s−t1+t−1s+1−st) .

Expanding and collecting terms gives

E=(1s−t)(t−1s+1−st)+(st−1)(s−t1+1−st)+(t1−s)(s−t1+t−1s)+3

=(1−s−tst)+s(s−t−1t)−t(s−t+1)s+3 .

In the first term, replace s+t with 1 , but in the other two terms replace 1 with s+t . Now we have,

E=2st+2s2t+2t2s+3=2+2(s3+t3)st+3 .

Factoring the sum of cubes,

E=2−2((s+t)2−3st)st+3 .

Backtracking, use s+t=1 , and so

E=2−2(1−3st)st+3=6+3=9

Step-by-step explanation: