Answer: 6 and 7
Step-by-step explanation:
Let the numbers be x and x + 1
We can form and equation as:
2(x²) + (x+1)² = 121
2x² + (x + 1)(x + 1) = 121
2x² + x² + x + x + 1 = 121
3x² + 2x = 121 - 1
3x² + 2x = 120
3x² + 2x - 120 = 0
3x² - 18x + 20x - 120 = 0
3x(x - 6) + 20(x - 6)
Therefore, x - 6 = 0
x = 0 + 6
x = 6
The numbers are 6 and 7
The two numbers given in the statement is required.
The two numbers can be [tex]6,7[/tex] or [tex]-\dfrac{20}{3},-\dfrac{17}{3}[/tex]
Let [tex]x[/tex] be the first number
[tex]x+1[/tex] be the next consecutive number
From the statement we get
[tex]2x^2+(x+1)^2=121\\\Rightarrow 2x^2+x^2+2x+1=121\\\Rightarrow 3x^2+2x-120=0\\\Rightarrow x=\dfrac{-2\pm \sqrt{2^2-4\times3\left(-120\right)}}{2\times3}\\\Rightarrow x=6,-\dfrac{20}{3}[/tex]
If [tex]x=6[/tex]
the other number is [tex]x+1=6+1=7[/tex]
If [tex]x=-\dfrac{20}{3}[/tex]
the other number is [tex]x+1=-\dfrac{20}{3}+1=-\dfrac{17}{3}[/tex]
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