# Khan/khan-exercises

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randRange( 2, 10 ) randRangeNonZero( -10, 10 ) randRange( 2, 10 ) randRangeNonZero( 2, 10 ) fractionReduce( D - B, A - C ) i18n._("No solution") (function() { if ( ( D - B ) / ( A - C) > 0 ) { return "<code>" + "x = " + fractionReduce( ( D - B ) * ( D - B), ( A - C ) * ( A - C) ) + "</code>"; } else { return NOSOLN; } })() (function() { var choices = []; for ( var i = 0; i < 4; i++ ) { var nOffset = randRange( 1, 10 ); var dOffset = randRangeExclude( 1, 10, [ C - A ] ); var choice = "<code>" + "x = " + fractionReduce( ( D - B + nOffset ) * ( D - B + nOffset ), ( A - C + dOffset ) * ( A - C + dOffset ) ) + "</code>"; choices.unshift( choice ); } if ( ( D - B ) / ( A - C ) > 0 ) { choices.shift(); choices.unshift( SOLUTION ); } choices = shuffle( choices ); choices.push( NOSOLN ); return choices; })()

Solve for x:

A\sqrt{x} + B = C\sqrt{x} + D

SOLUTION

• choice

Subtract C\sqrt{x} from both sides:

(A\sqrt{x} + B) - C\sqrt{x} = (C\sqrt{x} + D) - C\sqrt{x}

A - C\sqrt{x} + B = D

Subtract abs(B) from both sides:

(A - C\sqrt{x} + B) + -B = D + -B

A - C\sqrt{x} = D - B

Divide both sides by A - C.

\frac{A - C\sqrt{x}}{A - C} = \frac{D - B}{A - C}

Simplify.

\sqrt{x} = SIMPLIFIED

Square both sides.

\sqrt{x} \cdot \sqrt{x} = SIMPLIFIED \cdot SIMPLIFIED

SOLUTION

The principal root of a number cannot be negative. So, there is no solution.

Subtract A\sqrt{x} from both sides:

(A\sqrt{x} + B) - A\sqrt{x} = (C\sqrt{x} + D) - A\sqrt{x}

B = C - A\sqrt{x} + D

Subtract abs(D) from both sides:

B + -D = (C - A\sqrt{x} + D) + -D

B - D = C - A\sqrt{x}

Divide both sides by C - A.

\frac{B - D}{C - A} = \frac{C - A\sqrt{x}}{C - A}

Simplify.

SIMPLIFIED = \sqrt{x}

Square both sides.

SIMPLIFIED \cdot SIMPLIFIED = \sqrt{x} \cdot \sqrt{x}

SOLUTION

The principal root of a number cannot be negative. So, there is no solution.