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CBSE Class 10 Answered

Solve the equation (x+4)(x+7)(x+8)(x+11)+20=0
Asked by tdp8800 | 29 Apr, 2020, 07:19: AM
answered-by-expert Expert Answer
(x+4)(x+7)(x+8)(x+11)+20=0
(x+4)(x+11)(x+8)(x+7)+20=0
(x2+15x+44)(x2+15x+56)+20=0 ... (i)
Let y=x2+15x ... (ii)
(y+44)(y+56)+20=0
y2+100y+2464=0
y2+54y+46y+2484=0
y(y+54)+46(y+54)=0
(y+54)(y+46)=0
y=-54 or y=-46
Therefore,
x2+15x=-54 or x2+15x=-46
x2+15x+54=0 or x2+15x+46=0
x squared plus 9 x plus 6 x plus 54 equals 0 space space o r space space x equals fraction numerator negative 15 plus-or-minus square root of 225 minus 4 left parenthesis 46 right parenthesis end root over denominator 2 end fraction left parenthesis x plus 9 right parenthesis left parenthesis x plus 6 right parenthesis equals 0 space space o r space space x equals fraction numerator negative 15 plus-or-minus square root of 41 over denominator 2 end fraction subscript blank x equals negative 9 space o r space x equals negative 6 space o r space space x equals fraction numerator negative 15 plus-or-minus square root of 41 over denominator 2 end fraction
Answered by Renu Varma | 29 Apr, 2020, 02:23: PM

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