The foot of an extension ladder is 3 ft from a wall. The height that the ladder reaches on the wall and the length of the ladder
are consecutive integers. How long is the ladder?
1 answer:
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Solve the equations
first one
take the sqrt of both sides
x-y=√71
add y to both sides
x=y+√71
sub y+√71 for x in other part
(y+√71)²+y²=59
y²+2y√71+71+y²=59
2y²+2y√71+71=59
minus 59 both sides
2y²+2y√71+12=0
factor out 2
2(y²+y√71+6)=0
use quadratic equation or something
y=
and 
sub those for x
x=y+√71
note: √71=(2√71)/2
x=
,
or
x=
,
xy= times 
or times 
the result is -6 both times
xy=-6
first one
take the sqrt of both sides
x-y=√71
add y to both sides
x=y+√71
sub y+√71 for x in other part
(y+√71)²+y²=59
y²+2y√71+71+y²=59
2y²+2y√71+71=59
minus 59 both sides
2y²+2y√71+12=0
factor out 2
2(y²+y√71+6)=0
use quadratic equation or something
y=
sub those for x
x=y+√71
note: √71=(2√71)/2
x=
or
x=
xy=
the result is -6 both times
xy=-6