Math, asked by rithusruthi40, 1 year ago

If p = √3−√2 /√3+√2 and q = √3+√2 /√3−√2 , then find p^2+ q^2.


rithusruthi40: pls quickly

Answers

Answered by sonabrainly
1

This problem can be solved in 2 ways.


1st :-


=3‾√+2‾√3‾√−2‾√a=3+23−2


=(3‾√+2‾√)(3‾√+2‾√)(3‾√−2‾√)(3‾√+2‾√)=(3+2)(3+2)(3−2)(3+2)


=(3‾√+2‾√)23−2=(3+2)23−2


=((3‾√)2+(2‾√)2+2(3‾√)(2‾√)=((3)2+(2)2+2(3)(2)


=3+2+26‾√=3+2+26


=5+26‾√=5+26


=3‾√−2‾√3‾√+2‾√b=3−23+2


=(3‾√−2‾√)(3‾√−2‾√)(3‾√+2‾√)(3‾√−2‾√)=(3−2)(3−2)(3+2)(3−2)


=(3‾√−2‾√)23−2=(3−2)23−2


=((3‾√)2+(2‾√)2+−2(3‾√)(2‾√)=((3)2+(2)2+−2(3)(2)


=3+2−26‾√=3+2−26


=5−26‾√=5−26


Now


2+2a2+b2


We know that


(+)2=2+2+2(x+y)2=x2+y2+2xy


⟹2+2=(+)2−2⟹x2+y2=(x+y)2−2xy


If we take =x=a and =y=b then


2+2a2+b2


=(+)2−2=(a+b)2−2ab


=(5+26‾√+5−26‾√)2−2((5+26‾√)(5−26‾√))=(5+26+5−26)2−2((5+26)(5−26))


=(10)2−2(25−24)=(10)2−2(25−24)


Here we use identity (+)(−)=2−2(a+b)(a−b)=a2−b2


=100−2=100−2


=98=98


2nd :-


=3‾√+2‾√3‾√−2‾√a=3+23−2


=3‾√−2‾√3‾√+2‾√b=3−23+2


Now


=3‾√+2‾√3‾√−2‾√×3‾√−2‾√3‾√+2‾√ab=3+23−2×3−23+2


=1=1


+=3‾√+2‾√3‾√−2‾√+3‾√−2‾√3‾√+2‾√a+b=3+23−2+3−23+2


=(3‾√+2‾√)2+(3‾√−2‾√)2(3‾√+2‾√)(3‾√−2‾√)=(3+2)2+(3−2)2(3+2)(3−2)


=5+26‾√+5−26‾√3−2=5+26+5−263−2


=10=10


Now


(+)2=2+2+2(x+y)2=x2+y2+2xy


⟹2+2=(+)2−2⟹x2+y2=(x+y)2−2xy


Replacing =,=x=a,y=b


2+2=(+)2−2a2+b2=(a+b)2−2ab


=(10)2−2×1=(10)2−2×1


Replacing (+)=10(x+y)=10 and =1xy=1


=100−2=100−2


=98=98


Therefore 2+2=98a2+b2=98


It totally depends on you which method to use but I recommend the second one .


rithusruthi40: I don't understand:(
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