Math, asked by karryprue, 20 days ago

(If a³+ā³ = 50√7)
So prove that a = √6 + √7

(Here ā³ means a to the power minus 3)​

Answers

Answered by Yuvigirivc
1

Step-by-step explanation:

Given 0<50−−√−7<0.1 we have that, using y=50−−√ :

0<y3–3∗7∗y2+3∗72∗y−73<0.001 (a)

where we raised all sides of the inequality to the third power.

Now, we are interested in showing (50−−√+7)3 differs from an integer less than 0.001. Again using y=50−−√ we get for the above

(y+7)3=y3+3∗7∗y2+3∗72∗y+73 (b)

Now subtract a from b: 6∗7∗y2+2∗73 . Replacing y we get that

b−a=6∗7∗50+2∗73 , an integer.

Since a<0.001 then the difference between b and an integer is less than 0.001

Similar questions