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Solve the following equation by using factorisation method: `9x^(2)-6b^(2)x-(a^(4)-b^(4))=0.` |
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Answer» We may write, `-6b^(2)=3(a^(2)-b^(2))-3(a^(2)+b^(2)).` Also, `{3(a^(2)-b^(2))}xx{-3(a^(2)+b^(2)}=-(a^(4)-b^(4))` `:." "9x^(2)-6b^(2)x-(a^(4)-b^(4))=0` `implies" "9x^(2)+3(a^(2)-b^(2))x-3(a^(2)+b^(2))x-(a^(4)-b^(4))=0` `implies" "3x{3x+(a^(2)-b^(2))}-(a^(2)+b^(2)){3x+(a^(2)-b^(2))}=0` `implies" "{3x+(a^(2)-b^(2))}xx{3x-(a^(2)+b^(2))}=0` `implies" "3x+(a^(2)-b^(2))=0" or "3x-(a^(2)+b^(2))=0` `implies" "x=((b^(2)-a^(2)))/(3)" or "x=((a^(2)+b^(2)))/(3).` Hence, `((b^(2)-a^(2)))/(3)` and `((a^(2)+b^(2)))/(3)` are the required roots of the given equation. |
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