Two Numbers Square Relation

Two numbers are guessing. The second number is five times greater than the first number, and the square of the first number is equal to 3/5 of the second number. Find the sum of the two numbers and all its divisors.

Final Answer:

s₁ =  18
d₁ = 1, 2, 3, 6, 9, 18
s₂ =  0
d₂ =  

Step-by-step explanation:

$$\begin{gathered} b=5a \\ {a}^2=3/5b \\ {a}^2=3/5\cdot 5\cdot a \\ {a}^2=3/5\cdot 5\cdot a \\ {a}^2-3a=0 \\ p=1;q=-3;r=0 \\ D=q^2-4pr=3^2-4\cdot 1\cdot 0=9 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{3\pm \sqrt{9}}{2} \\ {a}_{1,2}=\frac{3\pm 3}{2} \\ {a}_{1,2}=1.5\pm 1.5 \\ {a}_1=3 \\ {a}_2=0 \\ {b}_1=5\cdot a_1=5\cdot 3=15 \\ {b}_2=5\cdot a_2=5\cdot 0=0 \\ {s}_1=a_1+b_1=3+15=18 \end{gathered}$$

Our quadratic equation calculator calculates it.

$d_1=1,2,3,6,9,18$

$s_2=a_2+b_2=0+0=0$

$$\begin{gathered} d_2\in R \\ {d}_2=d_2\ne 0= \end{gathered}$$

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