x 1 + 7 = 2 x 1 + 7 x = 2 x 2 2 x 2 − 7 x − 1 = 0 Δ = ( − 7 ) 2 − 4 ⋅ 2 ⋅ ( − 1 ) = 49 + 8 = 57 Δ = 57 x 1 = 2 ⋅ 2 − ( − 7 ) − 57 = 4 7 − 57 x 2 = 2 ⋅ 2 − ( − 7 ) + 57 = 4 7 + 57
R ec i p roc a l o f a n u mb er x : x 1 7 + x 1 = 2 x ∣ ∗ x 7 x + 1 = 2 x 2 − 2 x 2 + 7 x + 1 = 0 Δ = 7 2 − 4 ∗ ( − 2 ) ∗ 1 = 49 + 8 = 57 Δ = 57 x 1 = − 4 − 7 − 57 or x 2 = − 4 − 7 + 57
To find the number, we start with the equation 7 + X 1 = 2 X and rearrange it to form a quadratic equation 2 X 2 − 7 X − 1 = 0 . We then use the quadratic formula to find the values for X , which are X 1 = 4 7 − 57 and X 2 = 4 7 + 57 .
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