if x+2/3=7/3,then the value of x________
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Now we need to rationalise the following value to make it easier to solve,
x = \frac{2}{3 + \sqrt{7} } \times \frac{3 - \sqrt{7} }{3 - \sqrt{7} }
In the denominator we can use the identity which says :
(x + y)(x - y) = x ^{2} - {y}^{2}
x = \frac{6 - 2 \sqrt{7} }{(3) ^{2} - ( \sqrt{7}) ^{2} }
x = \frac{6 - 2 \sqrt{7} }{9 - 7}
x = \frac{6 - 2 \sqrt{7} }{2}
x = 3 - \sqrt{7}
Now we have to find the value of (x-3) and square the following,
(x - 3) = 3 - \sqrt{7} - 3
(x - 3) = - \sqrt{7}
Now squaring this value we get:
(x - 3) ^{2} = ( - \sqrt{7} ) ^{2}
(x - 3)^{2} = 7
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x = \frac{2}{3 + \sqrt{7} } \times \frac{3 - \sqrt{7} }{3 - \sqrt{7} }
In the denominator we can use the identity which says :
(x + y)(x - y) = x ^{2} - {y}^{2}
x = \frac{6 - 2 \sqrt{7} }{(3) ^{2} - ( \sqrt{7}) ^{2} }
x = \frac{6 - 2 \sqrt{7} }{9 - 7}
x = \frac{6 - 2 \sqrt{7} }{2}
x = 3 - \sqrt{7}
Now we have to find the value of (x-3) and square the following,
(x - 3) = 3 - \sqrt{7} - 3
(x - 3) = - \sqrt{7}
Now squaring this value we get:
(x - 3) ^{2} = ( - \sqrt{7} ) ^{2}
(x - 3)^{2} = 7
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Answered by
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Answer:
5/3
Step-by-step explanation:
x+2/3=7/3
3x+2 =7
3x=7-2
3x=5
x=5/3
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