If x=\frac{2}{3+\sqrt{7}}, then (x-3)^2 is equal to:
(a) 1
(b)3
(c)6
(d)7
help me to solve it.......
challenging ps for me......
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Hi,
Ignorance disclaimers ...
What is "\frac"? What is "\sqrt"?
Ignorance disclaimers ...
What is "\frac"? What is "\sqrt"?
Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
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Hi,
Unlikely to be GMAT level ...
x - 3 = (2/(3+sqrt{7})) - 3
= (-7-3sqrt(7))/(3+sqrt(7))
Squaring the previous term will lead to 7.
Unlikely to be GMAT level ...
x - 3 = (2/(3+sqrt{7})) - 3
= (-7-3sqrt(7))/(3+sqrt(7))
Squaring the previous term will lead to 7.
Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
4GMAT_Mumbai wrote:Hi,
Unlikely to be GMAT level ...
x - 3 = (2/(3+sqrt{7})) - 3
= (-7-3sqrt(7))/(3+sqrt(7))
Squaring the previous term will lead to 7.
thank u very much... can u explain me in step by step procedure please....
- kmittal82
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In problems like these, you have to rationalize the denominator i.e. make it into an integer if you can (look here https://www.math.unt.edu/mathlab/emathla ... action.htm)aarati wrote:4GMAT_Mumbai wrote:Hi,
Unlikely to be GMAT level ...
x - 3 = (2/(3+sqrt{7})) - 3
= (-7-3sqrt(7))/(3+sqrt(7))
Squaring the previous term will lead to 7.
thank u very much... can u explain me in step by step procedure please....
so, for this example, multiply and divide by 3 - sqrt(7)
x = 2/(3+sqrt(7)) * (3-sqrt(7))/(3-sqrt(7))
The denominator now takes the form a^2 - b^2, and in this case becomes 9 -7 = 2
x = 2*((3 - sqrt(7))/2
x - 3 = sqrt(7)
(x-3)^2 = 7
I think this sort of question could easily be in the GMAT, in the 500-600 level (I have seen a few in some practice tests which rely on denominator rationalisation)
thank u very much....this the only way to solve this type of problems....kmittal82 wrote:In problems like these, you have to rationalize the denominator i.e. make it into an integer if you can (look here https://www.math.unt.edu/mathlab/emathla ... action.htm)aarati wrote:4GMAT_Mumbai wrote:Hi,
Unlikely to be GMAT level ...
x - 3 = (2/(3+sqrt{7})) - 3
= (-7-3sqrt(7))/(3+sqrt(7))
Squaring the previous term will lead to 7.
thank u very much... can u explain me in step by step procedure please....
so, for this example, multiply and divide by 3 - sqrt(7)
x = 2/(3+sqrt(7)) * (3-sqrt(7))/(3-sqrt(7))
The denominator now takes the form a^2 - b^2, and in this case becomes 9 -7 = 2
x = 2*((3 - sqrt(7))/2
x - 3 = sqrt(7)
(x-3)^2 = 7
I think this sort of question could easily be in the GMAT, in the 500-600 level (I have seen a few in some practice tests which rely on denominator rationalisation)