Solution plz

x+a/x=1
x^2-x=-a

(x^2+x+a)/(x^3-x^2)=
(x+1+a/x)/(x^2-x)=
(1+1)/(-a)=-2/a

B

cos2pi/7+cos4pi/7+cos6pi/7=A
2A•sinpi/7=
2sinpi/7cos2pi/7+2sinpi/7•cos4pi/7+2sinpi/7•cos6pi/7=
sin3pi/7-sinpi/7+sin5pi/7-sin3pi/7+sin7pi/7-sin5pi/7

2A•sinpi/7=sinpi-sinpi/7
2A•sinpi/7=-sinpi/7
=>
A=-1/2

Cota+cotb+cotc=a^2+b^2+c^2/4delta

K+1=a^2+b^2+c^2/4delacotb

1/2 of acsinb=delta
4*1/2 of acsinb*cosb/SinB
2accosb
2acCosb=a^2+c^2-b^2
=2012b^2
So k+1=2014b^2/2012b^2
=1007/1006
K=1/1006

घन की सारी भुजा बराबर होती है।
इसिलए
+40%=2/5 5 7
+20%=1/5 5 6
+10%=1/10 10 11
घन के भुजा को समान बनाना होगा।
5:7=10:14
5:6=10:12
10:11=10:11




10 14
10 12
10 11
घन का पृष्टिय क्षेत्रफल 6(10)²
घनाभ का 2(lb+bh+hl)=

घन था इसीलिए रेश्यो लेकर सभी भुजा को बराबर 10 कर दिये
600--------2(168+132+154)=908

% increased 30800/600=51.33%😊

x^4-6x^2-1=0
x^4-1=6x^2
x^2-1/x^2=6
(x^2-1/x^2)^3=216
x^6-1/x^6-3•6=216
x^6-1/x^6=234

x^6-5x^2+5/x^2-1/x^6+5=
x^6-1/x^6-5(x^2-1/x^2)+5=
234-5•6+5=209

C

(a+b)/(b+c)=6/7
(a+b)/(c+a)=6/8

a+b+c=2a+2b+2c=
a+b+a+c+b+c=
a+b+7/6(a+b)+8/6(a+b)=28
21(a+b)=28•6

a+b=4•2=8

a+b+c=14 {(-) c=14-8=6

cos10cos50cos70-sin10sin50sin70=
sin80sin40sin20-cos80cos40cos20=
A-B

A=sin80sin40sin20=
1/2(cos40-cos120)•sin20=
1/4(sin60-sin20)+1/4sin20=
1/4sin60=sqrt(3)/8

B=cos80cos40cos20=
1/2(cos120+cos40)•cos20=
1/2•cos40cos20-1/4cos20=
1/4(cos60+cos20)-1/4cos20=
1/4cos60=1/8

A-B=sqrt(3)/8-1/8=(sqrt3-1)/8

D

a+b=1
a^2+b^2=3
(a+b)^2-2ab=3,
ab=-1
a^3+b^3=(a+b)((a+b)^2-3ab)=4

a^5+b^5=
(a+b)^5-5ab(a^3+b^3)-10a^2b^2(a+b)
a^5+b^5=1+5•4-10=11

Short method se

Demorvies theorem

2^10 multiply & divide

2^10*{√3/2+i/2}^10

2^10*{cos30°+isin30°}^10

Apply theorem

2^10*{cos(300°)+isin(300°)}=a+ib

2^10*{1/2+i(-√3/2)}=a+ib

2^10/2 - 2^10*(√3/2)=a+ib

2^9 - 2^9*√3i = a+ib

a=512
b=-512√3