anonymous
  • anonymous
Find three consecutive integers whose sum of their squares is 194. Write an equation, and solve the equation.Your equation MUST be an algebra equation with a variable.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
x^2+(x+1)^2+(x+2)^2 = 194 ===> 3x^2+(x^2+3x+1)+(x^2+4x+4) =194 ===> combining ===> 3x^2+6x+5=194 ===> x^2+2x-63 =0 ===> (x-7)(x+9)=0 ===> x=7 or x=-9 ===> x=7 ==> the numbers are 7 , 8 and 9
anonymous
  • anonymous
If the three integers are consecutive, then that means they are of the form\[x, x+1, x+2\]or more simply\[x-1,x,x+1\]If the sum of their squares is 194, then you can write:\[(x-1)^2+x^2+(x+1)^2=194\]From there, expand the brackets, and you'll end up with quite a simple equation which can be solved to find x (as well as x - 1, and x + 1). Take note of the fact that the question asks for "three consecutive \(\underline{integers}\)", which means they can be positive or negative. In fact, solving for x will get you two sets of numbers, which are equally valid.

Looking for something else?

Not the answer you are looking for? Search for more explanations.