Determine a from the equation a*a=-4 if a*b=ab+5(a+b)+21 .

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

a*a = -4

a*b = ab + 5(a+b) + 21

Now let us substitutw with a:

a*a = a^2 + 5(a+a) + 21

       = a^2 + 10a + 21 = -4

==> a^2 + 10a + 25 = 0

Now factor:

==> (a+5)^2 = 0

==> a = -5

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the unknown from the given equation, we need the definition of the operation of the composition law, definition which is given by the expression from enunciation.

We have to put the given expression in a more convenient manner.

a*b=(a+5)(b+5)-4

Now, we'll try to solve the equation a*a=-4

a*a=(a+5)(a+5)-4

-4=a^2+10a+25 - 4

a^2+10a+25=0

(a+5)^2=0

a1=a2=-5

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve for a in  the equation,a*a =-4 . The composition is a*b = ab+5(a+b)+21.

We rewrite  the equation by using the composition a inplace of b.

a*a = a*a+5(a+a)+25 = -4

a^2+10a+25-4 = 0

a^2+10a+21 = 0(a^2+7a

a^2+7a +3a +21 = 0

a(a+7)+3(a+7) = 0. Factor out a+7

(a+7)(a+3) = 0.

a+7 =0 gives a =-7

a+3 =0 gives a =-3.

So a=-7 or -3

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