Please solve the following problems:
X^{2}+x-12=0
SOLUTION
X^{2}+x-12=0
To solve for x in above problem we will calculate the real roots for the above quadratic equations by looking for two numbers whose sum is 1 and product is 12, then we equate them in the original equation and solve for x.
Sum = 1, product = 12 the two numbers are 4 and -3
We equate to have x^{2}+4x-3x-12=0
X(x+4)-3(x+4) = 0 thus x+4=0 and X= -4
OR X-3=0 AND X=3 thus x = 3 or -4
SOLUTION
Too solve for x we first equate the two values on both sides to the same base (base 2) then since the two are equal and with same base then their powers are equal thus we equate the powers and solve
Solve for x 2^{2x-4}=64 note 64=2^{6}
2^{2x-4}=2^{6 }thus 2x-4=6^{, }collect like terms together
2x= 6+4
2x=10 and diving by 2 both sides
2x/2 = 10/2, x=5
X=5
3cosx +2sin^{2}x=0
Solution
3cosx +2sin^{2}x=0
To solve for x we will use the trigonometric inequality stating that cos^{2}x + sin^{2}x =1 thus sin^{2}x=1-cos^{2}x thus we replace sin^{2}x with
1-cos^{2}x to have
3cosx+2(1-cos^{2}x) =0, 3cosx+2-2cos^{2}x = 0, let cos x be y
3y-2y^{2}+2=0, -2y^{2}=3y+2=0 then we solve the quadratic equation
Sum 3, product= -4 the two numbers are 4 and -1
-2y^{2}+4y-y+2=0 , -2y(y-2)-1(y-2) =0 ,(-2y-1)(y-2)=0
We equate in (-2y-1)=0 ,y=-1/2 or y-2=0 ,y=2
So -2y = -1, y= -1/2 or y-2=0 , y=2 recall y= cosx thus cosx=2
Recall y= cos (x) thus y=cos x = -1/2 or 2
x=cos^{-1 }2 which is absurd
X= cos^{-1 }-1/2 = 120 or 240
Thus value of x is120, x=120 or x = 240
Our motto is deliver assignment on Time. Our Expert writers deliver quality assignments to the students.
Get reliable and unique assignments by using our 100% plagiarism-free services.
The experienced team of AssignmentHippo has got your back 24*7. Get connected with our Live Chat support executives to receive instant solutions for your assignment problems.
We can build quality assignments in the subjects you're passionate about. Be it Programming, Engineering, Accounting, Finance and Literature or Law and Marketing we have an expert writer for all.
Get premium service at a pocket-friendly rate. At AssignmentHippo, we understand the tight budget of students and thus offer our services at highly affordable prices.