Câu 45 trang 59 Sách bài tập (SBT) Toán 9 tập 2
Giải các phương trình:
a) ({left( {x + 2} right)^2} – 3x – 5 = left( {1 – x} right)left( {1 + x} right))
b) ({left( {x – 1} right)^3} + 2x = {x^3} – {x^2} – 2x + 1)
c) (xleft( {{x^2} – 6} right) – {left( {x – 2} right)^2} = {left( {x + 1} right)^3})
d) ({left( {x + 5} right)^2} + {left( {x – 2} right)^2} + left( {x + 7} right)left( {x – 7} right) = 12x – 23)
Giải
a)
(eqalign{ & {left( {x + 2} right)^2} – 3x – 5 = left( {1 – x} right)left( {1 + x} right) cr & Leftrightarrow {x^2} + 4x + 4 – 3x – 5 = 1 – {x^2} cr & Leftrightarrow 2{x^2} + x – 2 = 0 cr & Delta = 1 – 4.2.left( { – 2} right) = 1 + 16 = 17 > 0 cr & sqrt Delta = sqrt {17} cr & {x_1} = {{ – 1 + sqrt {17} } over {2.2}} = {{sqrt {17} – 1} over 4} cr & {x_2} = {{ – 1 – sqrt {17} } over {2.2}} = – {{1 + sqrt {17} } over 4} cr} )
b)
(eqalign{ & {left( {x – 1} right)^3} + 2x = {x^3} – {x^2} – 2x + 1 cr & Leftrightarrow {x^3} – 3{x^2} + 3x – 1 + 2x = {x^3} – {x^2} – 2x + 1 cr & Leftrightarrow 2{x^2} – 7x + 2 = 0 cr & Delta = {left( { – 7} right)^2} – 4.2.2 = 49 – 16 = 33 > 0 cr & sqrt Delta = sqrt {33} cr & {x_1} = {{7 + sqrt {33} } over {2.2}} = {{7 + sqrt {33} } over 4} cr & {x_2} = {{7 – sqrt {33} } over {2.2}} = {{7 – sqrt {33} } over 4} cr} )
c)
(eqalign{ & xleft( {{x^2} – 6} right) – {left( {x – 2} right)^2} = {left( {x + 1} right)^3} cr & Leftrightarrow {x^3} – 6x – {x^2} + 4x – 4 = {x^3} + 3{x^2} + 3x + 1 cr & Leftrightarrow 4{x^2} + 5x + 5 = 0 cr & Delta = {5^2} – 4.4.5 = 25 – 80 = – 55