Answer: shorter: 24 longer: 41
Step-by-step explanation: we need to write an equation. x+(2x-7)=65. We don’t need the parentheses, but I put them so it would make it a bit more clear. Simplify: 3x-7=65. Add 7 to both sides: 3x=72. Divide by three: 72/3=24 Now we know the shorter piece is 24. 24x2-7=48-7=41. We know these are correct because 24+41=65
The extraneous solution is x=-1 and x=-6
Step-by-step explanation:
Given the question as;

Eliminate the root in the left hand side

solve the quadratic equation by factorization
Find multiples of 6 that add up to 7-------- 1*6
Rewrite the equation as;
x²+7x+6=0
x²+6x+x+6=0
x(x+6) +1 (x+6) =0
(x+1)(x+6) =0
x+1=0
x=-1
or
x+6=0
x=-6
The roots are, x=-1, and x=-6
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Quadratic equations : brainly.com/question/1332667
Keywords : extraneous, solution
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The first eight is in the thousands place and the second eight is in the hundreds place.