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Sagot :
The square of number is decreased by 15. This value is twice the original number. Find the number(s). The answer is:
x-15=2x
x-2x-15=0
(x-5)(x+3)=0
x=5x x=(-3)
x-15=2x
x-2x-15=0
(x-5)(x+3)=0
x=5x x=(-3)
The most common problems involving quadratic equations are finding the dimensions when the area is given.
Example:
Find the dimensions of a rectangular textbook whose length is 10cm longer than its width and covers an area of 375 cm².
Solution:
Let x be the width of the textbook
x+10 be the length of the textbook
A = width·length
375 = x (x+10)
375 = x² +10x
0 = x² +10x -375
0 = (x+25) (x-15)
x+25 = 0 ; x-15 = 0
x = -25 ; x = 15 (use x=15 because dimensions may never be negative)
Answer :
Width = 15 cm
Length = 25 cm (from x+10)
Example:
Find the dimensions of a rectangular textbook whose length is 10cm longer than its width and covers an area of 375 cm².
Solution:
Let x be the width of the textbook
x+10 be the length of the textbook
A = width·length
375 = x (x+10)
375 = x² +10x
0 = x² +10x -375
0 = (x+25) (x-15)
x+25 = 0 ; x-15 = 0
x = -25 ; x = 15 (use x=15 because dimensions may never be negative)
Answer :
Width = 15 cm
Length = 25 cm (from x+10)
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