Q. 855.0( 1 Vote )

There are three consecutive positive integers such that the sumÂ of thesquare of the first and the product of the other two is 154.Â What are theintegers?.

Answer :

Let the three consecutive positive integers be x, x + 1 and x + 2.

x

^{ 2 }+ (x + 1)(x + 2) = 154

x

^{ 2 }+ x

^{ 2 }+ 3x + 2 = 154

2x

^{ 2 }+ 3x - 152 = 0

2x

^{ 2 }+ 19x – 16x – 152 = 0

x(2x + 19) – 8(2x + 19) = 0

(x – 8)(2x + 19) = 0

x = 8 or

∴ The integers are 8, 9 and 10.

Checking:

8 ^{ 2 } + 9 × 10 = 64 + 90 = 154.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Get To Know About Quadratic Formula42 mins

Quiz | Knowing the Nature of Roots44 mins

Take a Dip Into Quadratic graphs32 mins

Foundation | Practice Important Questions for Foundation54 mins

Nature of Roots of Quadratic Equations51 mins

Getting Familiar with Nature of Roots of Quadratic Equations51 mins

Understand The Concept of Quadratic Equation45 mins

Balance the Chemical Equations49 mins

Quiz | Lets Solve Imp. Qs of Quadratic Equation43 mins

Champ Quiz | Quadratic Equation33 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

Draw the graph of 2x – 3y = 4. From the graph, find whether x = -1, y = -2 is a solution or not. (Final)

NCERT - MathematicsProve the following identities :

tan^{4}θ + tan^{2}θ = sec^{4}θ – sec^{2}θ

If, then find the values of sin θ and cos θ.

KC Sinha - MathematicsWrite the first three terms of the following sequences defined by:

KC Sinha - Mathematics