The greater number is 121
Step-by-step explanation:
The given is:
We need to find the greater number
Assume that the smaller number x and the greater number is y
∵ The smaller number is x and the greater number is y
∵ Their sum is 151
∴ x + y = 151 ⇒ (1)
∵ The lesser number is 19 more than the square root of the greater
number
∴ x = 19 + √y ⇒ (2)
- Substitute x in equation (1) by equation (2)
∵ (19 + √y) + y = 151
- Subtract 151 from both sides and re-arrange the terms from
the greatest power y
∴ y + √y - 132 = 0
Chang [tex]\sqrt{y}[/tex] to [tex]y^{\frac{1}{2}}[/tex] and substitute [tex]y^{\frac{1}{2}}[/tex] by h
∵ [tex]y^{\frac{1}{2}}[/tex] = h
∴ y = h²
- Substitute each y by h
∴ h² + h - 132 = 0
- Factorize it into two factors
∴ (h - 11) (h + 12) = 0
- Equate each factor by 0 to find h
∵ h - 11 = 0
- Add 11 to both sides
∴ h = 11
∵ h + 12 = 0
- subtract 12 from both sides
∴ h = -12
∵ h = [tex]y^{\frac{1}{2}}[/tex]
∴ [tex]y^{\frac{1}{2}}[/tex] = 11 and -12
∵ [tex]y^{\frac{1}{2}}[/tex] = √y
∴ √y = 11
∴ √y = -12 ⇒ rejected square root can't give -ve number
∴ √y = 11 only
- To find y square the both sides
∴ y = 121
The greater number is 121
Learn more:
You can learn more about the word problem in brainly.com/question/4034547
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