A Span Classsearchtermspan Classsearchtermcollectionspanspan of
A Span Classsearchtermspan Classsearchtermcollectionspanspan of
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To quickly assess the difficulty of the text, read a short excerpt:
\i cp^ — 'labp — ahc be taken for the root of (10), we have ab — (to — bo 2abc, ^, ^ .^-____ ^ QJ. — ... (11 ).
a (I From (4), x^=---^ — ^25 ^^^ since wi^=:a^zb2(m-|->^*, ^'^ n{9i±:2a) . . . (12). If we substitute for n in (12), its value as showm in (9), we shall get \aopKjp-±. A){[}-±Lb) ' ' ' ^ ^' If, in (13), M-e substitute iov p its first value in (11), or that in (ll')i using the -}- sign in the binomial factors of the denominator, wo shall find — \ {ab—ac—bcy—iabc' ^ '^'~Sabc(ar~ab—bc)(a...b--ac-i-bc)(ab^-ac—bc) ' ' * ^ ^* When the relation between a, b, c, is such as to make the numeri- (^al value of ic in (14) negative, (C) becomes [a^x'^-\-ax=[^ . . . (l')» b'x''-i-bx=[J . . . (2'), c'x'-^ex==^[J . . . (3')].. • (C); then ^ ^ (al, _a, _. L, cY-.^abc^ y ^ ^ Sabc(ab — ac — bc)(ab — ac-rbc){ab-rac — be) ' ' ' ^ ^ '' This shows that for such positive values of a, Z>, (", the conditions of (C) are im])ossible, by the general method, Avhei] positive an- wers are requii'cd, and that (C) must be changed to (C), that the problem may be possible; a'V, ^V, c^x-^ being three square num- bers, such, that if each be added to its respective root, the sums will be rational squares.
What to read after A Span Classsearchtermspan Classsearchtermcollectionspanspan of?
You can find similar books in the "Read Also" column, or choose other free books by James Matteson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
\i cp^ — 'labp — ahc be taken for the root of (10), we have ab — (to — bo 2abc, ^, ^ .^-____ ^ QJ. — ... (11 ).
a (I From (4), x^=---^ — ^25 ^^^ since wi^=:a^zb2(m-|->^*, ^'^ n{9i±:2a) . . . (12). If we substitute for n in (12), its value as showm in (9), we shall get \aopKjp-±. A){[}-±Lb) ' ' ' ^ ^' If, in (13), M-e substitute iov p its first value in (11), or that in (ll')i using the -}- sign in the binomial factors of the denominator, wo shall find — \ {ab—ac—bcy—iabc' ^ '^'~Sabc(ar~ab—bc)(a...b--ac-i-bc)(ab^-ac—bc) ' ' * ^ ^* When the relation between a, b, c, is such as to make the numeri- (^al value of ic in (14) negative, (C) becomes [a^x'^-\-ax=[^ . . . (l')» b'x''-i-bx=[J . . . (2'), c'x'-^ex==^[J . . . (3')].. • (C); then ^ ^ (al, _a, _. L, cY-.^abc^ y ^ ^ Sabc(ab — ac — bc)(ab — ac-rbc){ab-rac — be) ' ' ' ^ ^ '' This shows that for such positive values of a, Z>, (", the conditions of (C) are im])ossible, by the general method, Avhei] positive an- wers are requii'cd, and that (C) must be changed to (C), that the problem may be possible; a'V, ^V, c^x-^ being three square num- bers, such, that if each be added to its respective root, the sums will be rational squares.
What to read after A Span Classsearchtermspan Classsearchtermcollectionspanspan of?
You can find similar books in the "Read Also" column, or choose other free books by James Matteson to read onlineMoreLess
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