If log10x3+y3-log10x2-xy+y2+log10x3-y3-log10x2+xy+y2=log10221 where x,y are integers thenIf x=111 then y can be(A) ±111 - Maths - Relations and Functions

Question

I f   log 10 x 3 + y 3 - log 10 x 2 - x y + y 2 + log 10 x 3 -
y 3 - log 10 x 2 + x y + y 2 = log 10 221   w h e r e   x
, y   a r e   i n t e g e r s   t h e n I f   x
= 111   t h e n   y   c a n   b e ( A )  
± 111              
        B   ± 2    
                  C
  ± 110            
          D   ± 109 I f  
y = 2   t h e n   v a l u e   o f   x   c
a n   b e ( A )   ± 111      
                B  
± 15                
      C   ± 2      
                 
  D   ± 110

Neha Sethi · Accepted Answer

Dear student
Given:log10x3+y3-log10x2-xy+y2+log10x3-y3-log10x2+xy+y2=log10221⇒log10x3+y3x2-xy+y2+log10x3-y3x2+xy+y2=log10221⇒log10x+yx2-xy+y2x2-xy+y2+log10x-yx2+xy+y2x2+xy+y2=log10221⇒log10x+y+log10x-y=log10221⇒log10x2-y2=log10221⇒x2-y2=221⇒x2-y2=221 and y2-x2=221Case I : x2-y2=221When x=111⇒1112-221=y2⇒y2=1112-221=±110Case I : y2-x2=221When x=111⇒y2=221+x2⇒y2=221+1112⇒y=±111 approx
Similarly try other part
Note:logamn=logam-loganlogamn=logam+logana3+b3=a+ba2-ab+b2a3-b3=a-ba2+ab+b2
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I f log 10 x 3 + y 3 - log 10 x 2 - x y + y 2 + log 10 x 3 - y 3 - log 10 x 2 + x y + y 2 = log 10 221 w h e r e x , y a r e i n t e g e r s t h e n I f x = 111 t h e n y c a n b e ( A ) ± 111 B ± 2 C ± 110 D ± 109 I f y = 2 t h e n v a l u e o f x c a n b e ( A ) ± 111 B ± 15 C ± 2 D ± 110