Math, asked by Henry141, 1 year ago

please solve this question

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Answered by hukam0685
5

 {x}^{2}   + x - 6 \\ let \: the \: zeros \: are \:  \alpha  \: and \:  \beta  \\  \alpha  +  \beta  =   - 1 \\  \alpha  \beta  =  - 6
 \frac{1}{ \alpha }  +  \frac{1}{ \beta }  =  \frac{ \alpha  +  \beta }{ \alpha  \beta }  =  \frac{ - 1}{ - 6}  =  \frac{1}{6}
 { \alpha }^{2}  +  { \beta }^{2}  =  { \alpha }^{2}  +   { \beta }^{2}  + 2 \alpha  \beta  - 2 \alpha  \beta  \\  = ( { \alpha  +  \beta )}^{2}  - 2 \alpha  \beta  \\  = ( { - 1)}^{2}  - 2( - 6) \\  = 1 + 12 = 13
 ( { \alpha  -  \beta )}^{2}  = ( { \alpha  +  \beta )}^{2}  - 4 \alpha  \beta  \\  {( \alpha  -  \beta )}^{2}  =  {( - 1)}^{2}  - 4( - 6) \\  \:  \:  \:  \:    \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: = 1 + 24 = 25 \\  \\ ( \alpha  -  \beta ) =  \sqrt{25}  \\ ( \alpha  -  \beta ) = 5

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