# public Khan /khan-exercises

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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124         Radical equations

randRange( 2, 10 )            randRangeNonZero( -10, 10 )            randRange( 2, 10 )            randRangeNonZero( 2, 10 )            fractionReduce( D - B, A - C )                            (function() {                    if ( ( D - B ) / ( A - C) > 0 ) {                        return "<code>"                            + "x = "                            + fractionReduce( ( D - B ) * ( D - B), ( A - C ) * ( A - C) )                            + "</code>";                    } else {                        return "No solution";                    }                })()                            (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( "No solution" );                    return choices;                })()

Solve for x:

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

SOLUTION

• choice
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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

B > 0 ? "Subtract" : "Add" abs(B) B > 0 ? "from" : "to" 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

D > 0 ? "Subtract" : "Add" abs(D) D > 0 ? "from" : "to" 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.

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