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The product of two consecutive integers is 56. Find the integers.
The product of two consecutive integers is 56. Find the integers.
Exercise 6A | Maths | Selina | Solving (simple) Problems (Based on Quadratic Equations)
The product of two consecutive integers is 56. Find the integers.

let two continuous numbers to be $$ \[x\text{ }and\text{ }x\text{ }+\text{ }1.\]

So from the inquiry,

 

\[x\left( x\text{ }+\text{ }1 \right)\text{ }=\text{ }56\]

\[x2\text{ }+\text{ }x\text{ }\text{ }56\text{ }=\text{ }0\]

\[\left( x\text{ }+\text{ }8 \right)\text{ }\left( x\text{ }\text{ }7 \right)\text{ }=\text{ }0\]

Or,

\[x\text{ }+\text{ }8\text{ }=0\text{ }or\text{ }x-\text{ }7=0\]

hence,

\[x\text{ }=\text{ }-\text{ }8\text{ }or\text{ }7\]

In this way, the necessary numbers are \[\left( -\text{ }8,\text{ }-\text{ }7 \right)\text{ }or\text{ }\left( 7,\text{ }8 \right).\]

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