Algebra Quint @algebra_quint Channel on Telegram

Algebra Quint

09 Jan, 04:40

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

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Algebra Quint

08 Jan, 12:57

x√x - 2018√x = 2017
Find X - √x -1923

89

Algebra Quint

08 Jan, 12:53

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✅✅✅

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Algebra Quint

08 Jan, 12:51

Any short method

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Algebra Quint

07 Jan, 09:08

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✅

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Algebra Quint

07 Jan, 09:05

Put p=q=r=1
1=y+z
1=z+x
1=x+y

Find =(x/1+x)+(y/1+y)+(z/1+z)
==X+y+z/x+y+z==1

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Algebra Quint

27 Dec, 15:44

Put A=60,B=30,C=0
Ans=D

219

Algebra Quint

07 Nov, 03:42

A+b+c=√64+2*256=24
24(64-256)+3*987
Ans=-ve
Only B

467

Algebra Quint

03 Nov, 11:19

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

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Algebra Quint

06 Oct, 11:01

Set x=k+1 , y=k and z=k-1
k=2a

3k+3=3(4-a)

k+1=4-a

2a+1=4-a

a=1

633

Algebra Quint

22 Sep, 13:55

√(x²+y²+xy) - √(x²+y²-xy) = √2

So

(x²+y²+xy) + (x²+y²-xy) + 2√(x⁴+y⁴+x²y²) = 2

2(x²+y²) + 2√(x⁴+y⁴+x²y²) = 2

(x²+y²) + √(x⁴+y⁴+x²y²) = 1

√(x⁴+y⁴+x²y²) = 1 - (x²+y²)

x⁴+y⁴+x²y² = 1 + x⁴+y⁴+2x²y² - 2(x²+y²)

2(x²+y²) = x²y² + 1

2x² - x²y² + 2y² = 1

x²(2 - y²) - 4 + 2y² = 1 - 4

x²(2 - y²) - 2(2 - y²) = - 3

(2 - y²)(x² - 2) = -3

(2 - x²)(2 - y²) = 3

601

Algebra Quint

22 Sep, 13:55

√(x²+y²+xy)-√(x²+y²-xy)=√2

xy=1+√2.√(x²+y²-xy)

x²y²+1=2x²+2y²

2x²+2y²-x²y²-4=-3

x²(2-y²)-2(2-y²)=-3

(2-x²)(2-y²)=3

453

Algebra Quint

01 Sep, 15:36

(x+3)(x+4)x(x-1)+4=0
x(x+3)(x-1)(x+4)+4=0
(x²+3x)(x²+3x-4)+4=0
Put...... x²+3x=y
y(y-4)+4=0
y²-4y+4=0
y²-2y-2y+4=0
y(y-2)-2(y-2)=0
y=2

x²+3x=2
x-2/x=-3
x²+4/x²-4=9
x²+4/x²=13✅

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