Bonnycastle's Introduction to Algebra: Containing the Indeterminate and Diophantine Analysis, and the Application of Algebra to GeometryW.E. Dean, 1844 - 288 sayfa |
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Sayfa 89
... equation . Thus , if x = a + b , the terms are x , a , and b ; and the meaning of the expression is , that some ... cubic equations , biquadratic equations , & c . Thus , a quadratic equation is that in which the unknown quantity ...
... equation . Thus , if x = a + b , the terms are x , a , and b ; and the meaning of the expression is , that some ... cubic equations , biquadratic equations , & c . Thus , a quadratic equation is that in which the unknown quantity ...
Sayfa 127
... cubic equation , and therefore cannot be resolved by the ordinary rules of quadratics ; but such equations may ... cubic equation of the form x3 + ax = = b , b can be divided into two factors m and n , so that m2 + a = n , then the ...
... cubic equation , and therefore cannot be resolved by the ordinary rules of quadratics ; but such equations may ... cubic equation of the form x3 + ax = = b , b can be divided into two factors m and n , so that m2 + a = n , then the ...
Sayfa 129
... CUBIC EQUATIONS . A cubic equation is that in which the unknown quantity rises to three dimensions ; and , like quadratics , or those of the higher orders , is either simple or compound . A simple or pure cubic equation is of the form ...
... CUBIC EQUATIONS . A cubic equation is that in which the unknown quantity rises to three dimensions ; and , like quadratics , or those of the higher orders , is either simple or compound . A simple or pure cubic equation is of the form ...
Sayfa 130
... equation 3x3 - 13x2 + 4x + 16 = 0 , by assuming x = 3 , may be transformed into y3-13y2 + 42y + 144 = 0 , the roots of which are three times those of the former . - ED . 5. Let the equation x3 + 3 7 -х 9 130 CUBIC EQUATIONS .
... equation 3x3 - 13x2 + 4x + 16 = 0 , by assuming x = 3 , may be transformed into y3-13y2 + 42y + 144 = 0 , the roots of which are three times those of the former . - ED . 5. Let the equation x3 + 3 7 -х 9 130 CUBIC EQUATIONS .
Sayfa 131
... equation x3 + 3 7 -х 9 0 , be transform- 8 16 11 ed into another that shall want the second term . Ans . y3 + 169 = 3 4 6. Let the equation x + 8x3 - 5x2 + 10x - 4 = 0 , be ... CUBIC EQUATIONS . 131 Of the Solution of Cubic Equations,
... equation x3 + 3 7 -х 9 0 , be transform- 8 16 11 ed into another that shall want the second term . Ans . y3 + 169 = 3 4 6. Let the equation x + 8x3 - 5x2 + 10x - 4 = 0 , be ... CUBIC EQUATIONS . 131 Of the Solution of Cubic Equations,
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added Algebra answer arise arithmetical mean ax² binomial coefficients consequently cube root cubic equation decimal denominator denoted divisor equal EXAMPLES FOR PRACTICE expression factors find a number find the square find the sum find the value find two numbers former formula fourth fraction gallons geometrical geometrical progression give Given 2x given equation given number Given x² greater greatest common measure Hence infinite series last term less logarithms method multiplied negative nth root number of terms perpendicular PROBLEM proportion quadratic equation quadratic surd quotient rational remainder Required the number Required the sum required to divide required to find resolved result rule second term shillings side square number square root substituted subtracted surd third unknown quantity value of x Whence whole numbers yards