X+Y=15
XY=54
Find (x²-y²)
Answers
Answer:
±45
Step-by-step explanation:
Given X+Y = 15
XY=54 = X=54/Y
On substituting It in X+Y = 15 , we will get
(54/Y)+Y=15
On solving it we'll get the quadratic equation Y^2-15Y+54=0
on solving this we'll get Y to be 9 or 6
So on substituting it in X+Y=15, we will get X value to be 9 or 6 too.
Final result will be (X^2-Y^2) = 45 and -45
Answer:
given
X+Y=15
XY=54 ------(1)
if x+y=15
y = (15-x)
substituting value of y in eq(1)
x(15-x)=54
15x-x² = 54
x²-15x+54=0
x²-9x-6x+54=0
x(x-9)-6(x-9)=0
(x-9)(x-6)=0
x = 9,6
if x = 9
y=(15-x) =15-9 = 6
if x=6
y =(15-x) = 15-6 = 9
(x²-y²)
=9²-6² or 6²-9²
=81-36 or 36-81
=45 or -45
=±45
(x²-y²)= ±45 [plus or minus 45]
we cannot find exact values of x and y or (x²-y²) as given information is not enough
x=9 or 6
y=6 or 9
(x²-y²)= ±45