The value of the greater number minus the lesser number is
.
Further Explanation:
Let the greater positive number be
.
Let the lesser positive number be
.
The first condition is that the sum of
positive numbers is
.
The equation from the first condition can be expressed as,
![\boxed{x + y = 151}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%20%2B%20y%20%3D%20151%7D)
The second condition is that the lesser number is
more than the square root of the greater number.
![\boxed{y = 19 + \sqrt x }](https://tex.z-dn.net/?f=%5Cboxed%7By%20%3D%2019%20%2B%20%5Csqrt%20x%20%7D)
Substitute the value
in equation
to obtain the value of
.
![\begin{aligned} x +\left( {19+\sqrt x }\right)&= 151 \\ x + \sqrt x &= 151 - 19 \\ x + \sqrt x &= 132 \\ \sqrt x &= 132 - x \\ \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20x%20%2B%5Cleft%28%20%7B19%2B%5Csqrt%20x%20%7D%5Cright%29%26%3D%20151%20%20%5C%5C%20x%20%2B%20%5Csqrt%20x%20%26%3D%20151%20-%2019%20%20%5C%5C%20x%20%2B%20%5Csqrt%20x%20%26%3D%20132%20%5C%5C%20%20%5Csqrt%20x%20%26%3D%20132%20-%20x%20%20%5C%5C%20%5Cend%7Baligned%7D)
Square both the sides.
![\boxed{{\left( {\sqrt x } \right)^2} = {\left( {132 - x} \right)^2}}](https://tex.z-dn.net/?f=%5Cboxed%7B%7B%5Cleft%28%20%7B%5Csqrt%20x%20%7D%20%5Cright%29%5E2%7D%20%3D%20%7B%5Cleft%28%20%7B132%20-%20x%7D%20%5Cright%29%5E2%7D%7D)
Use the identity
.
![\begin{aligned} x &= {132^2} + {x^2} - 2 \times 132 \times x \\ x &= {132^2} + {x^2} - 264x \\ 0 &= {x^2} - 265x + 17424 \\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20x%20%26%3D%20%7B132%5E2%7D%20%2B%20%7Bx%5E2%7D%20-%202%20%5Ctimes%20132%20%5Ctimes%20x%20%5C%5C%20x%20%26%3D%20%7B132%5E2%7D%20%2B%20%7Bx%5E2%7D%20-%20264x%20%5C%5C%200%20%26%3D%20%7Bx%5E2%7D%20-%20265x%20%2B%2017424%20%5C%5C%5Cend%7Baligned%7D)
Solve the above quadratic equation to obtain the value of
.
![\begin{aligned} {x^2} - 121x - 144x + 17424 &= 0 \\ x\left( {x - 121} \right) - 144\left( {x - 121} \right) &= 0 \\ \left( {x - 121} \right) \times \left( {x - 144} \right) &= 0 \\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%20%7Bx%5E2%7D%20-%20121x%20-%20144x%20%2B%2017424%20%26%3D%200%20%5C%5C%20%20x%5Cleft%28%20%7Bx%20-%20121%7D%20%5Cright%29%20-%20144%5Cleft%28%20%7Bx%20-%20121%7D%20%5Cright%29%20%26%3D%200%20%5C%5C%20%20%5Cleft%28%20%7Bx%20-%20121%7D%20%5Cright%29%20%5Ctimes%20%5Cleft%28%20%7Bx%20-%20144%7D%20%5Cright%29%20%26%3D%200%20%5C%5C%5Cend%7Baligned%7D)
The value of
can be
and
.
The value of
cannot be possible as it doesn’t satisfies the two condition. Therefore the value of
is
.
The greater number is
.
Substitute
for
in equation
to obtain the value of
.
![\begin{aligned}121 + y &= 151 \\y &= 151 - 121 \\ y &= 30 \\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D121%20%2B%20y%20%26%3D%20151%20%5C%5Cy%20%26%3D%20151%20-%20121%20%5C%5C%20y%20%26%3D%2030%20%5C%5C%5Cend%7Baligned%7D)
The difference between the greater number and smaller number can be obtained as,
![\begin{aligned}\\\text{Difference} &= x - y \\ &= 121 - 30 \\ &= 91 \\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5C%5C%5Ctext%7BDifference%7D%20%26%3D%20x%20-%20y%20%5C%5C%20%26%3D%20121%20-%2030%20%5C%5C%20%26%3D%2091%20%5C%5C%5Cend%7Baligned%7D)
The value of the greater number minus the lesser number is
.
Learn more:
1. Learn more about unit conversion brainly.com/question/4837736
2. Learn more about non-collinear brainly.com/question/4165000
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Quadratic Equations
Keywords: sum, positive number, square root, lesser number, greater, number, quadratic equation, minus, sum of 2 positive numbers is 151, difference, lesser number is 19 more than the square root of greater, number, value.