# Category: Solved Questions Class 9

## If a^x=b^y=c^z and b^2=ac, then, show that y=2zx/(z+x)

If a^x=b^y=c^z and b^2=ac, then, show that y=2zx/(z+x)

## If a^x=b,b^y=c and c^z=a, then, prove that xyz=1, where a,b,c are real numbers and x,y,z are rational numbers.

If a^x=b,b^y=c and c^z=a, then, prove that xyz=1, where a,b,c are real numbers and x,y,z are rational numbers.

## If p and q are rational numbers and p-√q=(4+√2)/(3+√2), find the values of p and q.

If p and q are rational numbers and p-√q=(4+√2)/(3+√2), find the values of p and q.

## If x=√((5+2√6)/(5-2√6)) , show that x^2 (x-10)^2=1

If x=√((5+2√6)/(5-2√6)) , show that x^2 (x-10)^2=1

## Prove that √(-√3+√(3+8√(7+4√3) ) ) =2

Prove that √(-√3+√(3+8√(7+4√3) ) ) =2

## Show that 2(√2+√6)/(3√(2+√3) )=4/3

Show that 2(√2+√6)/(3√(2+√3) )=4/3

## If a=(√5-2)/(√5+2), show that a^4+a^(- 4) is an integer. Find it.

If a=(√5-2)/(√5+2), show that a^4+a^(- 4) is an integer. Find it.

## If x=√(3+2√2) , find the value of: x+1/x and x^2+1/x^2

If x=√(3+2√2) , find the value of: x+1/x and x^2+1/x^2

## If x=1/(√3-√2), prove that x^3+1/x^3 +2(x^2+1/x^2 )-9(x+1/x)=20

If x=1/(√3-√2), prove that x^3+1/x^3 +2(x^2+1/x^2 )-9(x+1/x)=20

## Find the value of x^3-6x^2+18x-22, where x=2-2^(1/3)+2^(2/3)

Find the value of x^3-6x^2+18x-22, where x=2-2^(1/3)+2^(2/3)

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