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# Algebra

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Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 11x - 2.  Compute (a - 4) + (b - 4).

Jan 6, 2024

#1
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7x^2 + x - 5 = 6x^2 - 11x - 2   simplifies to :

x^2 + 12x -3  = 0       which has roots     -6 +- sqrt (39)    ( Using Quadratic Formula with   a = 1    b =12   and  c= -3 )

then     a -4 =    -10 + sqrt (39)       and   b-4 =  -10 - sqrt (39)    adding these together :      =    -20

ANOTHER way :

we know that    - (a+ b ) = 12

or    a + b = -12          now subtract   -4  and -4   from both sides

(a-4) + (b-4) = -12 -4 -4

= -20

Jan 6, 2024

#1
+36900
+1

7x^2 + x - 5 = 6x^2 - 11x - 2   simplifies to :

x^2 + 12x -3  = 0       which has roots     -6 +- sqrt (39)    ( Using Quadratic Formula with   a = 1    b =12   and  c= -3 )

then     a -4 =    -10 + sqrt (39)       and   b-4 =  -10 - sqrt (39)    adding these together :      =    -20

ANOTHER way :

we know that    - (a+ b ) = 12

or    a + b = -12          now subtract   -4  and -4   from both sides

(a-4) + (b-4) = -12 -4 -4

= -20

ElectricPavlov Jan 6, 2024