Answer: while solving an equation involving fractions we eliminate the fraction by multiplying the LCD of all the denominators present in the equation . LCD means Least common Denominator so for this question when we try to eliminate the denominator we first try to find the LCM (2,4,6) because that will give us the LCD.
2=2
4=2·2
6=2·3
LCM = 2·2·3
LCM = 12
It means we need to multiply the 12 to each term of equation to eliminate the fractions before solving.
12
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.
The sum
can be written as:
,
<span>
from the binomial expansion formula: </span>
.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>
</span>
.
This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.
At x=5.4, the expression
, which is equivalent to
, takes it smallest value.
Substituting, we would find
=32.4 This is the smallest value of the expression.
For x=5.4, y=-3x+18=-3(5.4)+18=1.8.
Answer: (5.4, 1.8)
Step-by-step explanation: To evaluate functions substitute the given number or expression function's variable.
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