Find the number ab, when (a+b-3)-6a=-a^2-9.

3 Answers | Add Yours

isbeatbox's profile pic

isbeatbox | Student, Grade 11 | (Level 2) eNoter

Posted on




-7a=-9-b or 7a=9+b


then you do this




















neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

When (a+b-3)-6a= -a^2-9. To find ab. Solution: When a is given or known: b = =-a^2-9-a+3+6a = -a^2+5a+6. So , ab = a(-a^2+5a+6),if a is known we can get ab through a. When b is known: (a+b-3)-6a=-a^2-9.Or a^2-5a+6+b=0. So a = {5+sqrt[25-4(6+b)]^(1/2)}/2 Or a={5-sqrt[25-4(6+b)]^(1/2)}/2. Therefore, ab = b{5+sqrt[25-4(6+b)]6(1/2)}/2 = b{5+sqrt[1-b)]^(1/2)}/2.Or ab = b{5-sqrt[1-b)]}/2, when b is known.
giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

If we are moving the terms from the right side to the left side of the equality and if we are grouping them with the term "-6a", the result will be:

   (a+b-3) + (-6a+a^2+9)=0

The new group (-6a+a^2+9) could be written as (a-3)^2.

   (a+b-3) + (a-3)^2=0

The condition of equivalence between 2 expressions is that the equivalent terms from both expressions to be equal.

   (a+b-3)=0 and (a-3)^2=0

From (a-3)^2=0 it results that a-3=0, so a=3

By substituting the value of a into the relation  (a+b-3)=0, this one will become:

3+b-3=0, so b=0.

From both relations it results that the number ab=30.

We’ve answered 317,416 questions. We can answer yours, too.

Ask a question