if α,β are the roots of the equation x^{2}-3x+2=0 form an equation whose roots are (α+β)² & (α-β)²

Question

if α,β are the roots of the equation x^{2}-3x+2=0 form an equation whose roots are (α+β)² & (α-β)²

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Tài Đức 6 months 2021-07-31T12:34:41+00:00 1 Answers 6 views 0

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    2021-07-31T12:36:38+00:00

    Solution:

    Let’s find roots of x² – 3x + 2

    => x² – 3x + 2 = 0.

    => x² – x – 2x + 2 = 0.

    => x ( x – 1 ) -2 ( x – 1) = 0.

    => ( x – 1 ) ( x – 2 ) = 0.

    => x = 2, 1.

    Now

    • ( a + ß )² = (2+1)²=3²=9
    • ( a – ß )² = ( 2 – 1 )² = 1² = 1.

    So , equⁿ would be ,

    => x² – ( 9 + 1)x + 9×1=0.

    => x² – 10x + 9=0.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )