(Finding Two Numbers Given the Sum) Two consecutive positive odd numbers are such that the sum of their squares is 130. Find the two numbers,can you plz tell me how did this come?
Answers
Answer: 7 and 9
Step-by-step explanation: Let x be the the positive odd number and consecutive odd number be (x+2).
It is given that the sum of the squares of two consecutive numbers is 130, Therefore,
(x)2 + (x+2)2 = 130
x2 + x2 + 4 + 4x = 130 Therefore, (a + b)2 = a2 + b2 + 2ab)
2x2 + 4x + 4 - 130 = 0
2x2 + 4x - 126 = 0
2(x2 + 2x - 63) = 0
x2 + 2x - 63 = 0
x2 + 9x - 7x - 63 = 0
x(x + 9) -7 (x + 9) = 0
(x - 7) = 0, (x + 9) = 0
x = 7, x = -9
Since it is given that x is a positive odd number, thus x = 7.
Now, x + 2 = 7 + 2 = 9
Hence, the two consecutive positive odd numbers are 7 and 9.
Answer:
It is given that the sum of the squares of two consecutive numbers is 130, Therefore,
(x)² + (x+2)² = 130
x²+ x² + 4 + 4x = 130
Therefore, (a + b)² = a² + b² + 2ab)
2 * 2 + 4x + 4 - 130 = 0
2 * 2 + 4x - 126 = 0
2(x² + 2x - 63) = 0
x² + 2x - 63 = 0
x² + 9x - 7x-63=0
x(x + 9) - 7(x + 9) = o
(x - 7) = 0, (x + 9) = 0
x = 7 ,x = - 9
Since it is given that x is a positive odd
number, thus x = 7 Now, x + 2 = 7+2=9
Hence, the two consecutive positive odd numbers are 7 and 9.