Question

The sum of two numbers is 45 and the mean proportional between them is 18. The numbers
are
a) (15,30)
b) (32,13)
c) (36,9)
d) (25,20)​

Answer 1

Answer:

c) (36,9)

Step-by-step explanation:

let, the numbers are x and (45-x)

mean proportion between them is 18

So, x(45-x) = 18²

or, 45x-x² = 324

or, x²-45x+324 = 0

or (x-36)(x-9) = 0

then, 1st number = 36

2nd number = 45-36 = 9

Answer 2

Answer:

The two numbers are 36 and 9. Therefore, option c) is the suitable option.

Step-by-step explanation:

• To solve this problem, we must first know about the quadratic equation. A quadratic equation is an algebraic expression made of a polynomial of second degree in x.
• The quadratic equation is given by, $ax^2+bx+c=0$.
• Here, a, b, and c are known numbers and x is an unknown number.

Given:

Let's take the first number as x and the second number as y.

Therefore, the sum of two numbers,

$\begin{aligned}x+y&=45\\y&=45-x\end{aligned}$

Mean proportional, $\sqrt{x\times y} =18$

$\begin{aligned}x\times y&=18^{2}\\x\timesy&=324\\x\times(45-x)&=324\\45x-x^{2} &=324\\x^{2} -45x+324&=0\\(x-9)(x-36)&=0\\x&=9, 36\end{aligned}$

When x = 9, y = 36

When x = 36, y = 9

Conclusion:

The two numbers are 36 and 9. Therefore, among the given option, option c) is correct.

Know more about quadratic equations:

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