Question

if m+1/m=p-2 then prove that m2+1/m2=p2-4p+6

Answer 1

hope this will help you. . . . . . .

Answer 2

Complete question:

If $m - \frac{1}{m}$ = p - 2, then prove that $m^2 + \frac{1}{m^{2}} = p^2-4p+6$

Answer:

$m^2 + \frac{1}{m^{2}} = p^2-4p+6$ is proved

Step-by-step explanation:

Given,

$m - \frac{1}{m}$ = p - 2

To prove,

$m^2 + \frac{1}{m^{2}} = p^2-4p+6$

Solution:

Recall the identity

(a-b)² = a²  -2ab + b²

Given condition is $m - \frac{1}{m}$ = p - 2

Squaring on both sides we get

$(m - \frac{1}{m})^2$ = p - 2

Applying the identity (a-b)² = a²  -2ab + b²  we get

$m^2 + \frac{1}{m^2} - 2XmX\frac{1}{m} = (p-2)^2$

$m^2 + \frac{1}{m^2} - 2 = p^2 - 4p+4$

$m^2 + \frac{1}{m^2} = p^2 - 4p+4+2$

$m^2 + \frac{1}{m^2} = p^2 - 4p+6$

Hence proved

#SPJ3