Question

If a = xy^p-1 , b = xy^q-1 , c = xy^r-1 , prove that a^q-r b^r-p c ^p-q =1
Plzz ans fast !!

Answer 1

Answer:

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Answer 2

Answer:

Hi...☺

Here is your answer...✌

GIVEN :

a = x {y}^{p - 1} \:  ,\: b = x {y}^{q - 1} \: , \: c = x {y}^{r- 1}  

TO PROVE :

{a}^{q - r}   \:   {b}^{r - p}  \:  {c}^{p - q}  = 1

PROOF :

LHS

= {a}^{q - r}   \: {b}^{r - p} \:   {c}^{p - q}  \\  \\  =  {(x {y}^{p - 1} )}^{q - r }  \: {(x {y}^{q - 1} )}^{r - p}  \: {(x {y}^{r - 1} )}^{p - q}  \\  \\  =  {x}^{q - r}  {y}^{(p - 1)(q - r)}  \: {x}^{  r - p}  {y}^{(q - 1)(r - p)} \:  {x}^{p - q }  {y}^{(r - 1)(p - q )}  \\  \\  =  {x}^{q - r + r - p + p - q}   \: {y}^{(p - 1)(q - r) + (q - 1)(r - p) + (r -1 ) (p - q)}  \\  \\  =  {x}^{0} \:   {y}^{pq - pr - q + r + qr - pq - r + p + pr - qr - p + q}  \\  \\  = 1 \times  {y}^{0}  = 1  \times 1 \\  \\   = 1

= RHS -----[ Proved ]------

PLS MARK AS BRAINLIEST