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Show that if the roots of the equation `(a^2+b^2)x^2+2x(ac+bd)+c^2+d^2=0`are real, they will be equal

Text Solution

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`D=0`
`D= b^2 - 4ac = 2(ac+bd)^2 - 4(a^2+b^2)(c^2 + d^2)`
`= 4[ a^2c^2 + b^2d^2 + 2abcd - a^2c^2 - b^2c^2 - a^2d^2 - b^2d^2`
`=-4[b^2c^2 + a^2d^2 - 2abcd]`
`= -4[bc-ad]^2`
`x^2 >= 0`
`[bc - ad]^2 >= 0`
`=4[bc-ad]^2 <= 0`
...
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