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| 1. |
Solve for x: x^2+5x-(a^2+a-6)=0 |
| Answer» Given,\xa0{tex}x^2+5x-(a^2+a-6)=0{/tex}splitting {tex}a^2+a-6{/tex}{tex}\\Rightarrow{/tex}\xa0x2\xa0+ 5x - (a2\xa0+ 3a - 2a - 6) = 0{tex}\\Rightarrow{/tex}\xa0x2\xa0+ 5x - [ a(a + 3) - 2 (a + 3) ] = 0{tex}\\Rightarrow{/tex}\xa0x2\xa0+ 5x - (a + 3)(a - 2) = 0Now splitting the middle term{tex}\\Rightarrow{/tex}\xa0x2\xa0+ (a + 3)x -(a - 2)x - (a + 3) (a - 2) = 0{tex}\\Rightarrow{/tex}\xa0x [x + ( a + 3)] - ( a - 2)[ x + (a + 3)] = 0{tex}\\Rightarrow{/tex}\xa0[x + ( a + 3) ] [ x - (a - 2)] = 0\xa0{tex}\\Rightarrow{/tex}\xa0x + ( a + 3) = 0 or x - ( a - 2) = 0{tex}{/tex}\xa0Therefore,\xa0{tex}x=-(a+3) \\ {or} \\ (a-2){/tex} | |