For x to be real, discriminant of equation must be greater than equals to zero. ‌[2(y−1)]2−4(y−1)(4y−8)≥0 ⇒4(y−1)2−4(y−1)4(y−2)≥0 ⇒‌(y−1)2−(y−1)4(y−2)≥0 ⇒‌(y−1)[y−1−4y+8]≥0 ⇒‌(y−1)(−3y+7)≥0 ⇒‌y‌=1,‌
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∴‌‌(y−1)(−3y+7)≥0⇒y∈(1,‌
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] [∵. At y=1,x2+2x+4≠x2+2x+8] ‌∵‌‌y∈(1,‌