SOLUTION: Find three consecutive integers that the sum of twice the largest and the fourth power of the smallest is equal to the square of the remaining integer increased by 75. First int

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Find three consecutive integers that the sum of twice the largest and the fourth power of the smallest is equal to the square of the remaining integer increased by 75. First int      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 265600: Find three consecutive integers that the sum of twice the largest and the fourth power of the smallest is equal to the square of the remaining integer increased by 75.
First int __,__
Second int ___,___
Third int___,___
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the smallest of the three consecutive integers. Then next larger one must then be , and the largest must be .

The fourth power of the smallest is:

Twice the largest is:

The middle one squared increased by 75 is then:

Putting it all together:



Collect like terms:



Let , then:



Factor the quadratic:



Hence:



or



Which is to say:

which has no real number solutions

or



which means



or



Hence the three integers are either 3, 4, and 5 or -3, -2, and -1.

Check:





Answer checks.





Answer checks.

John