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प्रश्न
Solve `sqrt(y + 1) + sqrt(2y - 5)` = 3
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उत्तर
`sqrt(y + 1) + sqrt(2y - 5)` = 3 ...(squaring on both sides)
`(sqrt(y + 1) + sqrt(2y - 5))^2` = 32
`(sqrt(y + 1))^2 + (sqrt(2y - 5))^2 + 2(sqrt(y + 1))(sqrt(2y - 5))` = 9
`y + 1 + 2y - 5 + 2 sqrt((y + 1)(2y - 5))` = 9
`3y - 4 + 2 sqrt(2y^2 - 5y + 2y - 5)` = 9
`2sqrt(2y^2 - 3y - 5)` = 9 + 4 – 3y
= 13 – 3y ...(squaring on both sides)
`[2sqrt(2y^2 - 3y - 5)]^2` = (13 – 3y)2
4(2y2 – 3y – 5) = 169 + 9y2 – 78y
8y2 – 12y – 20 = 169 + 9y2 – 78y
8y2 – 9y2 – 12y + 78y – 20 – 169 = 0
–y2 – 66y – 189 = 0
y2 – 66y + 189 = 0
(y – 3) (y – 63) = 0
y = 3 or y = 63
The value of y is 3 and 63.
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