Algebra Quint
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1 549
x√x - 2018√x = 2017
x√x - 2018√x = 2018 - 1
x√x + 1 = 2018 + 2018√x
(√x)³ + (1)³ = 2018(√x + 1)
(√x + 1)(x - √x + 1) = 2018(√x + 1)
(x - √x + 1) = 2018
x - √x = 2017
So
x - √x - 1923
2017 - 1923
94
1 549
2x+3y-5z==18__(1)
3x+2y+z==29___(2)
X+y+3z==17____(3)
5×(iii)–[(i) +(ii)]
19z==38
z==2
x+y==17-6=11
2x+2y==22
2x+3y==28
y=6
x=5
atq.......
5×6+6×2+5×2==52✅✅✅
1 549
p³ = qy+rz
=>p²+x = px+qy+rz/p
=>q²+y = px+qy+rz/q
=>r²+z = px+qy+rz/z
=> x/(p²+x) + y/(q²+y) + z/(r²+z)
= (px+qy+rz)/(px+qy+rz) = 1✅
1 549
Set √(x-1/x)=a and √(1-1/x)=b
Then b+a=x
b²-a²=1-x
b-a=1/x-1
2a=x-1/x+1
2a=a²+1
(a-1)²=0
a=1
x-1/x=1
x²+1/x²=3
