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Answer:
let the two number be x and y.
Given: the product of two numbers is 450.
then: \(x\times y =450\) ......[1]
Also from the given condition that; the first number is half the second number. Also, x>y.
i.e, \(y=\frac{1}{2}x\)
Substitute this in equation [1];
\(x \times \frac{1}{2}x =450\)
or
\(\frac{1}{2}x^2 = 450\) [∴\(x^a \times x^b =x^{a+b}\)]
Multiply both sides by 2; we get
\(x^2 =450 \times 2\)
or
\(x^2=900\)
or
\(x=\sqrt{900} =30\)
Now, substitute this x value in [1], to solve for y;
\(30 \times y=450\)
Divide by 30 from both the sides, we get;
\(y = \frac{450}{30}=15\)
Therefore, the equation \(\frac{1}{2}x^2 = 450\) which can be used to find the value of x.
The greater number is x = 30.
The equation is used to find x is;
\(\rm x^2=900\)
The value of the greater number x is 30.
Given
The product of the two numbers is 450.
The first number is half the second number.
Let the first number be x and the second number be y.
The product of the two numbers is 450.
\(\rm x\times y = 450\)
The first number is half the second number.
\(\rm x = \dfrac{1}{2} y\)
Substitute the value of x in equation 1 from equation 2
\(\rm x \times y = 450\\\\x \times \dfrac{1}{2}x = 450\\\\x^2 = 450 \times 2\\\\x^2=900\\\\x=30\)
Substitute the value of x in equation 1
\(\rm x\times y=450\\\\30 \times y = 450\\\\y = \dfrac{450}{30}\\\\y = 15\)
Hence, the value of the greater number x is 30.
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