$sqrt (3t -7) = 2 - sqrt (3t + 1)?$ solve the radical equations, if possible.

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Answer 1 · 2017-04-15T05:23:47

$t=8/3$

$sqrt(3t-7)=2-sqrt(3t+1)$

$hArrsqrt(3t-7)+sqrt(3t+1)=2$

Now squaring each side, we get

$3t-7+3t+1+2sqrt((3t-7)(3t+1))=4$

or $6t+2sqrt((3t-7)(3t+1))=10$

or $sqrt((3t-7)(3t+1))=5-3t$

Squaring again we get

$(3t-7)(3t+1))=(5-3t)^2$

or $9t^2-18t-7=25-30t+9t^2$

or $-18t+30t=25+7$

or $12t=32$

i.e. $t=32/12=8/3$

sqrt (3t -7) = 2 - sqrt (3t + 1)? sqrt (3t -7) = 2 - sqrt (3t + 1)? solve the radical equations, if possible.