find three consecutive integers. the square of the largest is equal to the sum of the squares of the other two integers
Answer (2)
Answer:Finding Three Consecutive Integers Where the Square of the Largest Equals the Sum of the Squares of the Other TwoLet the three consecutive integers be x, x+1, and x+2, where x is the smallest integer.The square of the largest integer (x+2) must equal the sum of the squares of the other two integers (x and x+1):(x+2)2=x2+(x+1)2(x+2) 2 =x 2 +(x+1) 2 Expanding and simplifying:x2+4x+4=x2+2x+1+x2+2x+1x 2 +4x+4=x 2 +2x+1+x 2 +2x+1x2+4x+4=2x2+5x+2x 2 +4x+4=2x 2 +5x+20=x2+x−20=x 2 +x−2Solving this quadratic equation by factoring:x=−1±1+82=−1±32x= 2−1± 1+8 = 2−1±3 The only positive solution is x = 1. Therefore, the three consecutive integers are 1, 2, and 3.To check:(3)2=12+22=1+4=9(3) 2 =1 2 +2 2 =1+4=9The square of the largest integer (3) equals the sum of the squares of the other two integers (1 and 2).
Answer:3, 4, and 5Step-by-step explanation:5² = 3² + 4²25 = 9 + 1625 = 25
