Question

Find the integers of the word problem stated above.

Answer 1

Answer:

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Answer 2

$\huge{\fcolorbox{white}{lawngreen}{\rm{Word\;Problem}}}$

The sum of square of two consecutive positive integers is 145 find the integer

$\large{\fcolorbox{white}{lawngreen}{\rm{Solution:-}}}$

Let consecutive integers be x and (x + 1).

We have,

• ${\sf{{x}^{2} + ({x+1})^{2}}}$ = 145

Solve it,

= ${\sf{{x}^{2} + ({x+1})^{2}}}$ = 145

= ${\sf{{x}^{2} + {x}^{2} + 2x + 1 }}$ = 145

= ${\sf{ {2x}^{2} + 2x + 1 }}$ = 145

= ${\sf{ {2x}^{2} + 2x + 1}}$ - 145 = 0

= ${\sf{{2x}^{2} + 2x - 144}}$ = 0

= ${\sf{{x}^{2} + x - 72}}$ = 0

= ${\sf{{x}^{2} + 9x - 8x - 72}}$ = 0

= ${\sf{x ( x + 9) - 8 (x + 9)}}$ = 0

= ${\sf{( x + 9) (x - 8) }}$ = 0

• Solve into two possible cases

= x + 9 = 0

= x - 8 = 0

• The equation has two solution

= x = -9

= x = 8

•°• The two integers so obtained are -9 and 8.

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