Algebra Task (Math Problem Sample)

Please solve the following problems:
Question 1
Find the value of
(7-6.35)÷6.5+9.9(1.2÷36+1.2÷0.25-1516)÷16924
Use BODMAS rule to solve this equation
Convert mixed numbers to improper fractions:
1516=2116
Hence (7-6.35)÷6.5+9.9(1.2÷36+1.2÷0.25-2116)÷16924
Subtract 7-6.35=0.65
=0.656.5+9.91.236+1.20.25-211616924
Apply fraction rule:abc=a.cb
=0.656.5+9.924(1.236+1.20.25-2116169
0.656.5+9.9.1691.236+1.20.25-2116
Take the denominator and use LCM to solve it
=1.236+1.20.25-2116
=1.2+172.8-189436
Add the numbers: 1.2+172.8-1894=174-1894=5074
=507436=50736×4=507144=16948 =3.52083
=169(0.656.5+9.9)24×3.52083
=169(0.1+9.984.5
But 16984.5=2 and 0.1+9.9=10.0
Hence 2×10=20
Question 2.
Solve for x
x2+1x-4+x2-1x+3=23
Find the LCM and multiply throughout
x2+1x-4+x2-1x+3=231
LCM of x-4,x+3,1 is (x-4)(x+3)
x2+1x-4(x-4)(x+3)+x2-1x+3(x-4)(x+3)=231(x-4)(x+3)
Cancel similar expressions to obtain
x2+1x+3+x2-1x-4=23(x-4)(x+3)
Expand each expression to simplify them
Apply FOIL method a+bc+d=ac+ad+bc+bd
x2+1x+3
a=x2,b=1,c=x,d=3
=(x2.x+x2.3+1.x+1.3=x3+3x2+x+3
x2-1x-4
a=x2 ,b=-1,c=x,d=-4
=x2.x+x2-4+-1x+-1.-4=x3-4x2-x+4
23x-4x+3
x-4x+3
a=x,b=-4,c=x,d=3
xx+3x-4x-4.3=x2-x-12
=23(x2-x-12)
=23x2-23x-276
Hence
x3+3x2+x+3+x3-4x2-x+4=23x2-23x-276
Collect like terms and regroup the expression
2x3-24x2+23x+283=0
Use Newton-Raphson Approximation to solve the above equation. It uses iterative methods to find one root
xn+1=xn-fxnf'xn where fxn=2x3-24x2+23x+283 and f'xn=6x2-48x+23
Let x0=-5
fx0=2-53-24-52+23-5+283=-682
f'x0=6-52-48-5+23=413
x1=-5--682413=-3.34866
∆x1=-3.34866--5=1.65133
fx1=2-3.348663-24-3.348662+23-3.34866+283=-138.24638
f'x0=6(-3.34866)2-48-3.34866+23=251.01755
x2=-3.34866--138.24638251.01755=-2.79792
∆x2=-2.79792--3.34866=0.55074
x2=-2.79792 ∆x2=0.55074
fx2=2-2.797923-24-2.797922+23-2.79792+283=-13.03983
f'x3=6(-2.79792)2-48-2.79792+23=204.27065
x3=-2.79792--13.03983204.27065=-2.73408
∆x3=-2.73408--2.79792=0.0